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Highly Frustrated Magnetism (wHFM21)

In recent years it has become possible to grow high-quality epitaxial thin (<4nm - 500 nm) films of spin ice materials such as Dy$_{2}$Ti$_{2}$O$_{7}$ on isostructural Y$_{2}$Ti$_{2}$O$_{7}$ substrates by pulsed laser deposition [1]. Intriguingly, while these thin films show various experimental signatures associated with spin ice systems, they appear to become ordered at temperatures below 1 K instead of retaining the residual Pauling entropy that is characteristic of bulk spin ices. It has been proposed that this behaviour may be explained by epitaxial strain which breaks the degeneracy of the six ice-rule obeying vertices that comprise the Coulomb phase of bulk spin ice, favouring an antiferromagnetic ground state. In this way spin ice thin films realise exactly-solved Rys F-model of statistical physics, which has an unusual ordering transition of the Berezinskii–Kosterlitz–Thouless class [2,3]. Here we shall explore the phenomenology of the F-model in applied fields using both exact results and Bethe lattice methods to identify experimental signatures of F-model physics that could be measured in thin film spin ice systems [4]. In particular we explore topological aspects of the F-model and how these relate to experimental quantities in spin ice, artificial spin ice and water ice. Finally, we present sub-Kelvin susceptibility measurements for thin films of Dy$_{2}$Ti$_{2}$O$_{7}$ and compare these with predictions from the F-model. [1] L. Bovo et al., Restoration of the third law in spin ice thin films, Nature Commun. 5, 3439 (2014). [2] L. Bovo et al., Phase transitions in few-monolayer spin ice films, Nature Commun. 10, 1219 (2019). [3] R. J. Baxter, Exactly Solved Models in Statistical Mechanics, 1st Ed., Academic Press, London (1989). [4] D. M. Arroo and S. T. Bramwell, Experimental Measures of Topological Sector Fluctuations in the F-Model, arXiv: 2010.05839 (2020, accepted Phys. Rev. B).

Spin-nematic order is an unconventional order involving quadrupole moments instead of magnetic dipole moments. Quadrupolar order parameter makes the spin-nematic order difficult to detect with conventional probes. We study magneto-elastic coupling and its effect on the fractional change in sound velocity as technique to identify spin ferronematic(ferro-quadrupolar) order. From the perspective of microscopics, we consider a bi-linear bi-quadratic spin-1 Hamiltonian on a triangular lattice. We examine the self energy due to magnon-phonon interaction and find out the temperature dependence of fractional change in sound velocity in the ferronematic phase. The temperature dependence of fractional change in the sound velocity in the paramagnetic phase is also calculated. To complement the microscopics approach, we write the Landau theory for the coupling of strains, dipoles, quadrupoles and magnetic field. Using the Landau theory, we draw conclusions about the fractional change in sound velocity and fractional change in length at the transition to a ferronematic. We also examine whether magneto-elastic coupling can be used to distinguish between ferronematic and anti-ferronematic orders.

Analyzing the magnetic structure factor of a field demagnetized artificial square ice, qualitative deviations from what would predict the square ice model are observed. Combining micromagnetic and Monte Carlo simulations, we demonstrate that these deviations signal the presence of interactions between nanomagnets that extend beyond nearest neighbors. Including further neighbor, dipolar-like couplings in the square ice model, we find that the first seven or eight coupling strengths are needed to reproduce semi-quantitatively the main features of the magnetic structure factor measured experimentally. An alternative, more realistic numerical scenario is also proposed in which the ice condition is slightly detuned. In that case as well, the features evidenced in the experimental magnetic structure factor are only well-described when further neighbor couplings are taken into account. Our results show that long range dipolar interactions are not totally washed out in a field demagnetized artificial square ice, and cannot be neglected as they impact the magnetic correlations within the ice manifold.

There is recent interest in fracton phases of matter, which host quasiparticles characterized by emergent mobility restrictions and may feature a variety of exciting phenomena. Here we explore the properties of a one-dimensional model of strongly correlated electrons that describes a liquid of singlet pairs in which single electron excitations behave as fractons. Hallmarks of fractonic behavior are observed, including localization of single electron excitations and a tendency to attractive clustering. These confirm the important role played by the dipole conservation law in the phase diagram of such model.

We discuss a special solution of the 16 vertex model via a mapping on a planar Ising model. The solution can then be obtained via a novel reformulation of the Fisher decoration of the lattice, and reduced to the determinant of a 32x32 matrix.

Artificial spin ice (ASI) is a magnetic metamaterial designed to exhibit frustration. It consists of an array of magnetostatically interacting nanomagnets arranged in a geometry that prevents these interactions to be all satisfied simultaneously. They were originally conceived to replicate, in an artificial manner, interesting frustration induced phenomena found in natural frustrated magnets known as spin ices. One of the most remarkable is the emergence of quasiparticles similar to magnetic monopoles when such materials are excited above the ground state. In ASI this behavior is experimentally reproduced by subjecting the system to a magnetization cycle. The magnetization reversal proceeds by creation of one-dimensional strings of flipped nanomagnets, referred as Dirac strings, that host the magnetic monopoles at their ends. This behavior was also already reproduced by Monte Carlo based simulations, where the nanomagnets are treated as Ising variables and a phenomenological random switching field distribution is employed. In this work, we reproduced the same behavior using a more fundamental approach, that was lacking in literature, based on micromagnetic simulations, applied particularly to a large scale (more than a thousand magnets) kagome lattice arrangement of ASI. We regarded a more realistic description of the shape of each nanomagnet, including its finite size and roughness at the edges, in such a way that no a priori switching field distribution was required but that came out naturally. Our simulations still predict a new, bidimensional reversal mechanism that occurs if the magnetic field is applied below a certain critical angle.

Non-equilibrium properties of quantum materials present many intriguing properties, among them athermal behavior, which violates the eigenstate thermalization hypothesis. Such behavior has primarily been observed in disordered systems. More recently, experimental and theoretical evidence for athermal eigenstates, known as "quantum scars" has emerged in non-integrable disorder-free models in one dimension with constrained dynamics [1]. I will focus on directions that my group is pursuing in the context of geometrically frustrated magnets. First, I show the existence of quantum scar eigenstates and investigate their dynamical properties in many simple two-body Hamiltonians with staggered interactions, involving ferromagnetic and antiferromagnetic motifs, in arbitrary dimensions. These magnetic models include simple modifications of widely studied ones (e.g., the XXZ model) on a variety of lattices [2]. I will demonstrate our ideas by focusing on the two dimensional frustrated spin 1/2 kagome antiferromagnet, which was previously shown to harbor a special exactly solvable point with "three-coloring" ground states in its phase diagram [3]. Next, I discuss how Hilbert space fragmentation naturally arises in many frustrated magnets with low-energy ``ice manifolds'' which gives rise to a broad range of relaxation times for different initial states [4]. We study the Balents-Fisher-Girvin Hamiltonian where the frustration is encoded in the ice rules, and a phenomenological three-coloring model with loop excitations, both with constrained Hilbert spaces. We characterize the formation of the fragmented Hilbert space of these Hamiltonians, their level statistics, and initial state dependence of relaxation dynamics. I will also suggest experimental platforms for observing this physics. [1] H. Bernien et al., Nature 551, 579–584 (2017); C. Turner et al., Nature Physics 14, 745-749 (2018) [2] K. Lee, R. Melendrez, A. Pal, H.J. Changlani, Phys. Rev. B 101, 241111(R) (2020) [3] H.J. Changlani, D. Kochkov, K. Kumar, B. Clark, E. Fradkin, Phys. Rev. Lett. 120, 117202 (2018) [4] K. Lee, A. Pal, H.J. Changlani, arXiv:2011.01936 (2020)

Quantum spin liquids are the epitomes of highly entangled quantum states of matter. However, their detection in quantum materials remains elusive, due to the competition with more conventional magnetically ordered states. In this talk, I will propose a novel mechanism to stabilise quantum spin liquid states by exploiting the coupling of quantum magnets to the quantised light of an optical cavity. The interplay between the quantum fluctuations of the electromagnetic field and the strongly correlated electrons results in a tunable long-range interaction between localized spins. This cavity-induced frustration robustly stabilises spin liquid states, which occupy an extensive region in the phase diagram spanned by the range and strength of the tailored interaction. Remarkably, this occurs even in originally unfrustrated systems, as we showcase for the Heisenberg model on the square lattice.

Spin-orbital liquids are quantum disordered states in systems with entangled spin and orbital degrees of freedom. % We study exactly solvable spin-orbital models in two dimensions with selected Heisenberg-, Kitaev-, and $\Gamma$-type interactions, as well as external magnetic fields. These models realize a variety of spin-orbital-liquid phases featuring dispersing Majorana fermions with Fermi surfaces, nodal Dirac or quadratic band touching points, or full gaps. In particular, we show that Zeeman magnetic fields can stabilize nontrivial flux patterns and induce metamagnetic transitions between states with different topological character. Solvable nearest-neighbor biquadratic spin-orbital perturbations can be tuned to stabilize zero-energy flat bands. We discuss in detail the examples of $\mathrm{SO}(2)$- and $\mathrm{SO}(3)$-symmetric spin-orbital models on the square and honeycomb lattices, and use group-theoretical arguments to generalize to $\mathrm{SO}(\nu)$-symmetric models with an arbitrary integer $\nu > 1$. These results extend the list of exactly solvable models with spin-orbital-liquid ground states and highlight the intriguing general features of such exotic phases. Our models are thus excellent starting points for more realistic modellings of candidate materials.

Frustrated $J_1 - J_2$ model in one-dimension exhibits magnetization plateaus at $m = 1/3$ in applied magnetic field. The two-dimensional Kagome lattice also shows magnetization plateaus at $m=1/9$, 1/3, 5/9 and 7/9. There are experimental results of magnetization plateaus in case of spin chains like Cu$_3$(CO$_3$)$_2$(OH)$_2$ andCu$_3$(CO$_3$)$_2$(OH)$_2$. In this talk I will present our studies on magnetization plateaus in a skewed ladder system formed by fusing alternatively five and seven membered rings. We employ Exact Diagonalization (ED) and Density matrix Renormalization Group (DMRG) techniques in this study. We observe magnetization plateaus at magnetization $m = M/M_{\mathrm{max}} = 1/4$, 1/2 and 3/4 where $M_s$ is the saturation magnetization and M is the observed magnetization. The occurrence of these plateaus are consistent with Oshikawa, Yamanaka and Affleck (OYA) condition $ S \, p (1 - m) \in $ $\mathbb{Z} $ where $S$ is the spin of the site, $p$ is the number of sites in a unit cell and $\mathbb{Z}$ represents the set of positive integers. By calculating the spin densities and bond-orders, we explain why these plateaus appear (at least for large J1). These results are also consistent with the perturbation calculation for large values $J1$.

Ankur Dhar [OIST], Ludovic Jaubert[CNRS], Tsumoru Shintake and Nic Shannon [OIST] The special properties of spin ice have given a new context to fundamental physics questions, such as the the existence of magnetic monopoles [1], and the possibility of emergent electric fields in a spin liquid with dynamics [2, 3] However, while there is compelling evidence for the existence of magnetic monopoles in spin ice, the direct observation of a point-like source of magnetic field in these systems remains an open challenge. One technique that could make direct observation a possibility is electron holography, which combines atomic-scale resolution with extreme sensitivity to magnetic vector potentials, through the Aharonov-Bohm effect. In this talk we present the first experimental holographic measurements of magnetic monopoles in artificial spin ice, together with numerical simulations of equivalent experiments on a thin film of pyrochlore spin ice. In the case of artificial spin ice, we show how holograms can be used to estimate local magnetic charge, gaining new insights into the phenomenon of "moment fragmentation" on a honeycomb lattice. In the case of pyrochlore spin ice, we demonstrate that holographic experiments performed with ideal resolution are capable of resolving both magnetic monopoles and their dynamics, including the emergence of electric fields associated with fluctuations of closed loops of spins. We build upon these results to provide concrete estimates of the spatial and phase resolution needed to image monopoles in a real experiment. These results suggest that the direct observation of both magnetic monopoles and emergent electric fields in pyrochlore spin ice is a realistic possibility in an electron microscope with sufficiently high phase resolution. [1] C. Castelnovo, R. Moessner, and S. L. Sondhi, Nature 451, 42 (2008). [2] R. Moessner and S. L. Sondhi, Phys. Rev. B 68, 184512 (2003). [3] M. Hermele, M. P. A. Fisher, and L. Balents, Phys. Rev. B 69, 064404 (2004).

The spin ice materials Ho2Ti2O7 and Dy2Ti2O7 are experimental and theoretical exemplars of highly frustrated magnetic materials. However, the effects of an applied uniaxial pressure are not well studied, and here we report magnetization measurements of Ho2Ti2O7 under uniaxial pressure applied in the [001], [111] and [110] crystalline directions. The basic features are captured by an extension of the dipolar spin ice model. We find a good match between our model and measurements with pressures applied along two of the three directions, and extend the framework to discuss the influence of crystal misalignment for the third direction. The parameters determined from the magnetization measurements reproduce neutron scattering measurements we perform under uniaxial pressure applied along the [110] crystalline direction. In the detailed analysis we include the recently verified susceptibility dependence of the demagnetizing factor. Our work demonstrates the application of a moderate applied pressure to modify the magnetic interaction parameters. The knowledge can be used to predict critical pressures needed to induce new phases and transitions in frustrated materials, and in the case of Ho2Ti2O7 we expect a transition to a ferromagnetic ground state for uniaxial pressures above 3.3 GPa.

The surface of a topological insulator hosts Dirac electronic states with the spin-momentum locking, which constrains spin orientation perpendicular to electron momentum. As a result, collective plasma excitations in the interacting Dirac liquid manifest themselves as coupled charge- and spin-waves. Here we demonstrate that the presence of the spin component enables effective coupling between plasma waves and spin waves at interfaces between the surface of a topological insulator and insulating magnet. Moreover, the helical nature of spin-momentum locking textures provides the phase winding in the coupling between the spin and plasma waves that makes the spectrum of hybridized spin-plasma modes to be topologically nontrivial.

Exciton polaritons are light-matter hybrid quasiparticles that can form a Bose-Einstein condensate (BEC) at ambient laboratory conditions. The hybridisation arises from the strong coupling of excitons (bound electron-hole pairs) and photons in a cavity, which results in an effectively spin-1/2 configuration. Combined with the inherent polarisation splitting and weak anisotropy, a synthetic spin-orbit coupling and magnetic field can occur in this system. I will present our experimental study on the effect of the emergent synthetic gauge field on the excitation spectrum of an interaction-dominated exciton-polariton BEC. The excitations dispersions are strongly anisotropic due to the gauge field and the dependence of exciton-polariton interaction on the spin (singlet or triplet) configuration. Furthermore, I will present the effect of the inherent photonic losses in microcavities on the single-particle dispersions of exciton polaritons. Losses render the synthetic gauge field non-Hermitian, resulting in a novel topology that has no counterpart in conservative systems.

The existence and stability of spin-liquid phases represent central topics in the field of frustrated magnetism. In the last few years, a large theoretical effort has been devoted to proposing and studying frustrated spin models which could host spin-liquid ground states. Although several examples of well-established spin-liquid phases are now available, the question of the stability of these states to the coupling between spins and lattice distortions (i.e. phonons) has been scarcely investigated. As suggested by the well-known one-dimensional case, the effect of lattice deformations could cause a Peierls instability of spin-liquid phases towards the formation of valence-bond order. We present a variational framework for the study of spin-phonon models in which lattice distortions affect the exchange interaction between the spins. Our method, based on Jastrow-Slater wave functions and Monte Carlo sampling, provides a full quantum treatment of both spin and phonon degrees of freedom. We first assess the accuracy of our variational scheme by comparing our results for the spin-Peierls chain with other numerical methods [1]. Then, we discuss preliminary results on the effects of the spin-phonon coupling on the spin liquid phases of two-dimensional frustrated models. [1] F. Ferrari, R. Valenti, F. Becca, Phys. Rev. B 102, 125149 (2020).

We propose that the hyperfine coupling can destabilize electronic ordering, giving rise to interesting physics, like temperature-driven reentrance of magnetic order. We bring forward the tetragonal rare-earth spin system, with a $g$-anisotropy. Our calculation establishes that in such a system, it is possible to produce a magnetic order in the hard direction/plane. Then, the hyperfine coupling destabilizes this order. Our calculations further show that at zero temperature the ordered phase suffers maximum destabilization, which decreases with temperature resulting in a reentrance to the same ordered phase. We derive the detailed nature of the quantum phase boundary, estimating the shifts it undergoes in the presence of hyperfine coupling in different temperature regions of the phase diagram. We also discuss in details about the possible realizations of this physics.

We study the frustrated classical Heisenberg model on the triangular lattice, searching for phases breaking the point group symmetry of the lattice. By using a field theoretic framework, we scan the $J_2 - J_3$ parameter space with $J_1$ ferromagnetic, where $J_i$ represents the $i$-th nearest neighbor coupling. In addition to detect lattice-nematic phases, we also find a novel symmetry broken state, which shows an extended maximum in the spin correlation function.

We investigate the interplay between spatial anisotropy and further exchange interactions in the spin-1/2 Heisenberg antiferromagnetic model on a triangular lattice. We use the Schwinger boson theory by including Gaussian fluctuations above the mean-field approach. The phase diagram exhibits a strong reduction of the long-range collinear and incommensurate spiral regions with respect to the mean-field ones. This reduction is accompanied by the emergence of its short-range order counterparts, leaving an ample room for zero-flux and nematic spin-liquid regions. Remarkably, within the neighborhood of the spatially isotropic line, there is a range where the spirals are so fragile that only the commensurate 120∘ Néel ones survive. The good agreement with recent variational Monte Carlo predictions gives support to the rich phase diagram induced by spatial anisotropy.

Arrays of interacting nanomagnets known as Artificial Spin Ice (ASI) have allowed the design of geometrically frustrated exotic collective states not found in natural magnets. A key emergent description of fundamental excitations in ASIs is that of magnetic monopoles - mobile quasiparticles that carry an effective magnetic charge. These charge excitations can interact with each other and with applied magnetic fields via the magnetic analog of the electronic Coulomb interaction, representing the emergence of a range of novel phenomena, including the possibility of "magnetricity". While the presence of monopoles in ASI has been observed in pioneering imaging measurements, dynamical studies of monopole kinetics, and (especially) the ability to tune continuously through monopole-rich regimes in thermal equilibrium, remain at an early stage. Here we use a high-bandwidth magneto-optical noise spectrometer to passively "listen" to spontaneous magnetization fluctuations in thermally active square ASI. The noise reveals specific regions in the field-dependent phase diagram where the density of mobile monopoles increases well over an order of magnitude compared with neighboring regimes, a consequence of the field-tunable tension on the Dirac strings connecting mobile monopoles. Moreover, detailed noise spectra demonstrate that monopole kinetics are minimally correlated (i.e., most diffusive) in this plasma-like regime [1]. Discovery of on-demand monopole regimes with tunable kinetic properties opens the door to new probes of magnetic charge dynamics and provides a new paradigm for studies of magnetricity in artificial magnetic materials. [1] M. Goryca et al., arXiv:2008.08635 (2020).

In a crystal structure of Ca$_{5}$Ir$_{3}$O$_{12}$ which is a hexagonal with noncentrosymmetric (P-62m No. 189), 1D chains of edge-sharing IrO$_{6}$ octahedra along $c$-axis form triangular lattice in $c$-plane [1]. The average valence of Ir ions is +4.67; the ratio of Ir$^{4+}$ : Ir$^{5+}$ is 1 : 2. This intermediate valence of Ir ions can lead to the geometrical frustration of charge on both the triangular lattice in $c$-plane and 1D chains along $c$-axis. Ca$_{5}$Ir$_{3}$O$_{12}$ shows a semi-conductivity [1,2], and nonlinear electrical conductivity along $c$-axis is also discovered [3, 4]. Ca$_{5}$Ir$_{3}$O$_{12}$ shows an antiferromagnetic ordering below 7.8 K and a second order phase transition at 105 K [1]. Our recent Raman scattering experiments to the single crystal of Ca$_{5}$Ir$_{3}$O$_{12}$ have shown that the phase transition at 105 K is a structural phase transition [5], however, the origin of the phase transition is not clear at present. Therefore, the crystal and magnetic structure at low temperature have not been yet clarified. We have investigated the magnetic properties of the single crystal Ca$_{5}$Ir$_{3}$O$_{12}$ both along $c$-axis and $c$-plane. The temperature dependence of magnetic susceptibility was measured under the field up to 70 kOe using a SQUID magnetometer (Quantum Design, MPMS3). We revealed the anisotropic magnetic phase diagram of Ca$_{5}$Ir$_{3}$O$_{12}$ both along $c$-axis and $c$-plane. We will present the experimental results in this presentation. [1] M. Wakeshima, et al., Solid State Commun., 125, 311 (2003). [2] G. Cao, et al., Phys. Rev. B 75, 134402 (2007). [3] K. Matsuhira, et al., J. Phys. Soc. Jpn. 87, 013703 (2018). [4] H. Hanate, et al., J. Mann. Mag. Mater. 498, 166203 (2020). [5] T. Hasegawa, et al., accepted in J. Phys. Soc. Jpn.

Artificial quantum systems hold promise for simulating exotic frustrated magnets which have frustrated attempts by classical computers. However, current and near term devices have architectures restricted to particular classes of Hamiltonians. Here, we consider the most natural frustrated model that can be embedded into the Chimera graph of the D-Wave 2000Q: the fully frustrated transverse field Ising model on the 4-8 lattice. By a combination of analytic and quantum Monte Carlo methods, we show that the model exhibits a rich phase diagram including quantum order-by-disorder induced $Z_8$ and $Z_6$ symmetry breaking states, as well as corresponding Kosterlitz-Thouless (KT) phases at finite temperature. Preliminary D-Wave simulations point towards a KT phase with quasi-long-range order, while direct access to the ordered ground state requires lower temperatures than currently available.

The kagome lattice in two-dimensional (2D) hosts both Dirac-like and flat electronic bands, offering a rich space to realize strongly correlated electronic phases of matter. There is growing effort in the theoretical prediction and experimental realization of these phenomena in organic and metal-organic nanomaterials using the versatile protocols of bottom-up self-assembly. Here we report the synthesis of a 2D metal-organic kagome framework via coordination of copper atoms with di-cyano-anthracene (DCA) molecules on an Ag(111) noble metal surface. We observe Kondo screening of magnetic moments from unpaired electrons in the 2D MOF partially filled valence band via low-temperature scanning tunneling spectroscopy. These observations are consistent with supporting DFT+U calculations. Our work paves the way for atomically precise, meso-scaled 2D metal-organic frameworks for strongly correlated electronics.

Recently, we have explored a variety of compounds where non-coplanar magnetic order occurs on characteristic length scales comparable to the size of a single crystallographic unit cell. An important theme of our research is the importance of competing interactions in realizing these complex magnetic ground states, and searching for analogies between highly frustrated magnetic insulators and metallic magnets. Using material platforms as disparate as oxides and rare earth intermetallics, we target the universal physics of Berry-curvature driven topological Hall effect (THE) arising due to magnetic order with finite scalar spin chirality $S_i \cdot (S_j\times S_k)$. Previous work described the THE driven by scalar spin chirality as a Berry curvature field acting on wavepackets of Bloch electrons propagating through a canted magnetic texture with long period (continuum limit). In contrast to this established scenario, our focus is on materials where the periodicity of the magnetic unit cell is extremely small ($<5$ nanometers) and where the real-space picture breaks down. Instead, a momentum-space theory of the THE is expected to be more appropriate for an adequate description, where the Bloch waves themselves are modified due to scalar spin chirality. We will present ultra-high resolution measurements of electric and thermoelectric transport, in particular of the Hall and Nernst effect, in the abovementioned systems. Contact is made to supporting numerical calculations, as well as neutron and resonant elastic x-ray scattering experiments. Thus, we aim to develop new phenomenology of transport signatures characteristic in the limit of entangled real-space canted magnetism and momentum space Berry curvature, with implications for the broader field of correlated topological matter.

We investigate the finite-temperature properties of the $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice in the presence of an external magnetic field. We focus on the highly frustrated regime around $J_2 \approx J_1/2$. The $H$-$T$ phase diagram is investigated with particular emphasis on the finite-temperature transition into the ``up-up-up-down'' state that is stabilized by thermal and quantum fluctuations and manifests itself as a plateau at one half of the saturation magnetization in the quantum case. Furthermore, we discuss the enhanced magnetocaloric effect associated to the ground-state degeneracy that arises at the saturation field for $J_2=J_1/2$. Computations for the spin-1/2 system are carried out using finite-temperature Lanczos and quantum typicality approaches.

The rare-earth magnet TmMgGaO4 is proposed to be an intrinsic quantum Ising magnet described by the antiferromagnetic transverse field Ising model (TFIM) on a triangular lattice, where the relevant degrees of freedom are the nondegenerate dipole-multipole doublets of the Tm$^{3+}$ ions and the transverse field has an intrinsic origin from the weak splitting of the doublet. We compare this special doublet of Tm$^{3+}$ with the dipole-octupole Kramers doublet. We study the proposed effective model for the Tm-based triangular lattice and consider the effects of external magnetic fields and finite temperatures. From the orthogonal operator approach, we show that the TFIM with the three-sublattice intertwined ordered state agrees with the experiments and further clarify the discrepancy in the numbers of the magnetic sublattices and the measured magnon branches. We make specific predictions for the evolution of the magnetic properties with the external magnetic field. Furthermore, we demonstrate that an emergent U(1) symmetry emerges in thermal melting of the underlying orders and at the criticality, and summarize the previously known signatures related to the finite-temperature Berezinskii-Kosterlitz-Thouless physics. We discuss the broad relevance of intrinsic quantum Ising magnets to many other systems, especially Tm-based materials.

Structural, electronic, and magnetic properties of modified cubic spinel compound LiNi$_{0.5}$Mn$_{1.5}$O$_{4}$ are studied via x-ray diffraction, resistivity, DC and AC magnetization, heat capacity, neutron diffraction, $^7$Li nuclear magnetic resonance, magnetocaloric effect, magnetic relaxation, and magnetic memory effect experiments. We stabilized this compound in a cubic structure with space group $P4_{3}32$. It exhibits semiconducting character with an electronic band gap of $\Delta/k_{\rm B} \simeq 0.4$~eV. The interaction within each Mn$^{4+}$ and Ni$^{2+}$ sub-lattice and between Mn$^{4+}$ and Ni$^{2+}$ sublattices is found to be ferromagnetic (FM) and antiferromagnetic (AFM), respectively. This leads to the onset of a ferrimagnetic transition at $T_{\rm C} \simeq 125$~K. The reduced values of frustration parameter ($f$) and ordered moments reflect magnetic frustration due to competing FM and AFM interactions. From the $^7$Li NMR shift vs susceptibility plot, the average hyperfine coupling between $^7$Li nuclei and Ni$^{2+}$ and Mn$^{4+}$ spins is calculated to be $\sim 672.4$~Oe/$\mu_{\rm B}$. A detailed critical behaviour study is done in the vicinity of $T_{\rm C}$ using modified-Arrott plot, Kouvel-Fisher plot, and universal scaling of magnetization isotherms. The magnetic phase transition is found to be second order in nature and the estimated critical exponents correspond to the 3D XY universality class. A large magneto-caloric effect is observed with a maximum value of isothermal change in entropy $\Delta S_m \simeq - 11.3$~J/Kg-K and a maximum relative cooling power of $RCP \simeq 604$~J/Kg for 9~T magnetic field change. The imaginary part of the AC susceptibility depicts a strong frequency dependent hump at $T=T_{\rm f2}$ well below the blocking temperature $T_{\rm b}\simeq120$~K. The Arrhenius behaviour of frequency dependent $T_{\rm f2}$ and the absence of ZFC memory confirm the existence of superparamagnetism in the ferrimagnetically ordered state.

The Kitaev honeycomb model is a paradigmatic model hosting a quantum spin liquid phase where physical spins fractionalize into itinerant Majorana fermions and $Z_2$ gauge fluxes (visons).The model is exactly solvable thanks to the static nature of the visons. This feature is lost once we include more naturally occurring spin exchange interactions or a magnetic field. In the perturbative regime, such terms render the visons dynamic. We use perturbation theory to calculate the leading contribution to the dispersion of a single isolated vison due to the symmetric off-diagonal interaction ($\Gamma$), a weak uniform magnetic field and Heisenberg exchange interaction ($J$). We calculate the hopping amplitudes of a vison dressed with gapless Majorana fermions. To linear order in perturbation strength, the magnetic field and $\Gamma$ terms are found to give the vison a finite hopping amplitude in the FM Kitaev model but not the AFM model. The effect of the Heisenberg interaction is studied using a variational method, which presents intriguing insights.

The exactly solvable spin-1/2 Kitaev model on the honeycomb lattice features a $\mathbb Z_2$ quantum spin liquid (QSL) ground state with fractionalized excitations. Extended Kitaev models furthermore include non-Kitaev isotropic and anisotropic interactions, that can suppress the QSL ground state in favor of magnetic order. Such models are thought to describe Kitaev candidate materials like, e.g., $\alpha$-RuCl$_3$ and A$_2$IrO$_3$ ($A$ = \{Na, Li\}). While $\alpha$-RuCl$_3$ orders magnetically, various unconventional observations have been made experimentally. Especially under a magnetic field, which suppresses magnetic order at $\sim 7\,$T, much scrutiny lies in the nature of the magnetic state. We analyze the spectroscopic and thermodynamic response in $\alpha$-RuCl$_3$ in the context of extended Kitaev models. We also show first results on magnetoelastic coupling. Our methods include exact diagonalization techniques and first-principles simulations.

We construct the general theoretical framework to design or predict a variety of magnon-based topological physics in insulating antiferromagnets. It is known that for insulating ferro/ferrimagnets, a thermal Hall effect is induced by magnons propagating in an intrinsic U(1) gauge field, which is, however, a phenomenon restricted to frustrated pyrochlore or kagome lattices [1]. We show that insulating antiferromagnets can host a thermal Hall effect in non-frustrated square lattices, since its origin is an effective SU(2) gauge field generated from an inversion-symmetry breaking of crystals, similarly to the anomalous Hall effect in spin-orbit (SO) coupled electronic systems. In fact, by regarding the two species of magnons defined on antiferromagnetic sublattices as pseudo-up/down spin degrees of freedom, one can realize as rich phenomena as SO electronic systems; magnon Rashba-Dresselhaus effect, nonreciprocity of magnon bands, anomalous SU(2) thermal Hall effect, and edge modes protected by Z2 topological invariant [2,3]. We develop a formulation to extract the explicit form of the pseudo-SO coupling from the typical Bogoliubov-de Gennes type of antiferromagnetic spin-wave Hamiltonian, which allows us to discover the emergent nontrivial spin textures in the Kitaev-type of antiferromagnet [4]. [1] S, Fujimoto, Phys. Rev. Lett. 103, 047203 (2009), H. Katsura et al., Phys. Rev. Lett. 104, 066403 (2010), Y. Onose et al., Science 329, 297 (2010), T. Ideue et al., Phys. Rev. B 85, 134411 (2012). [2] M. Kawano et al., Commum. Phys. 2, 27 (2019). [3] M. Kawano and C. Hotta, Phys. Rev. B 99, 054422 (2019). [4] M. Kawano and C. Hotta, Phys. Rev. B 100, 174402 (2019).

Borates with the general formula Ba$_3$Ln(BO$_3$)$_3$ are of interest for optical applications. The compounds with larger lanthanide ions, Ln = Pr–Tb, crystallise in a trigonal unit cell with the Ln$^{3+}$ ions arranged in closely spaced chains, while smaller ions (Y, Dy–Lu) favour a hexagonal unit cell with a quasi-2D triangular lattice of Ln$^{3+}$ ions. Certain intermediate-sized ions can exhibit either polymorph, depending on the synthesis temperature. The magnetic behaviour of the hexagonal borates has been investigated using susceptibility measurements, revealing predominantly antiferromagnetic interactions with no sharp magnetic ordering transitions above 2 K, suggesting that these compounds are magnetically frustrated. In this contribution I will discuss our most recently obtained data on the compound Ba$_3$Tb(BO$_3$)$_3$, including heat capacity at $T \geq 0.4$ K, elastic neutron scattering at $T=0.08-5$ K, and inelastic neutron scattering with reference to crystal electric field modelling.

We study the stability of Kitaev quasiparticles in the presence of a perturbing Heisenberg interaction as a Fock space localization phenomenon. We identify parameter regimes where Kitaev states are localized, fractal, or delocalized in the Fock space of exact eigenstates, with the first two implying quasiparticle stability. Finite-temperature calculations show that a vison gap, and a nonzero plaquette Wilson loop at low temperatures, both characteristic of the deconfined Kitaev spin-liquid phase, persist far into the neighboring phase that has a concomitant stripy spin-density wave (SDW) order. The key experimental implication for Kitaev materials is that below a characteristic energy scale, unrelated to the SDW ordering, Kitaev quasiparticles are stable.

Non-Abelian band topology was recently shown to govern non-trivial braiding rules for band nodes in the momentum space of certain space-time-inversion-symmetric solids. In this talk, we apply the non-Abelian band topology to triply degenerate nodal points (triple points) -- the rotation symmetry-protected intermediates between Weyl and Dirac points. In particular, we show that rotation-symmetry breaking converts certain triple points into multi-band nodal links. To derive this relation, we first classify triple points in space-time-inversion-symmetric systems with negligible spin-orbit coupling, and then use quaternion invariants to identify the symmetry criteria which ensure the described conversion. Based on the above, we outline several further implications of triple-point configurations. These are, in particular, non-trivial Euler and Stiefel-Whitney monopole charges, which facilitate higher-order topology with hinge charges. Finally, we present triple-point material candidates, identified via first-principles calculations, which we predict to exhibit the described physics.

Electronic materials with topologically nontrivial band structure have been greatly explored in the past two decades. Except for the Chern insulators and the Weyl semimetals, all other topological phases discovered so far are protected by certain symmetries, including the time-reversal and the crystalline symmetries. Similar to electrons, bosonic particles such as magnons and phonons can also exhibit nontrivial surface/edge modes originating from their band topology. However, unlike the electronic systems, the symmetry protection mechanism for magnon systems has rarely been studied. The established knowledge of symmetry protections for electronic systems does not seem to be directly applicable in magnon systems. As a result, it seems to be difficult to understand the symmetry enriched/enforced band degeneracies in topological magnon systems. Here, in this talk, we show that by using pseudo-time-reversal symmetry defined for magnon system, one can similarly study the symmetry protected/enriched band degeneracy in magnon systems as in the electronic systems. As an example, we show in a concrete material that pseudo-time-reversal and pseudo-glide symmetry can jointly protect a Dirac nodal line with nontrivial surface states.

Artificial spin ices that are comprised of dipolar-coupled nanomagnets offer the possibility to create designer geometrical frustration and to manipulate the inter-nanomagnet interactions[1,2]. Here we create an ASI lattice consisting of paired nanomagnet stadia, which are coupled antiferromagnetically with a controllable gap between the two paired nanomagnets, as the building blocks on a Kagome lattice, referred to as an AK-ASI. We use MuMax3[3] micromagnetic simulation to predict the complex energy landscape of the demagnetized ASI systems and experimentally verify the real-space magnetic ordering in the system using high-resolution Lorentz transmission electron microscopy. In addition, by combining the experimental data with a Heisenberg Hamiltonian model and Monte Carlo simulations, we have derived key insights into the governing inter-island coupling. Results show that the magnetic phase can be altered between a classical antiferromagnetic phase and a classical spin liquid phase through tuning the competition between the neighboring interactions. These findings provide an insight and a pathway into tunable antiferromagnetic coupling of artificial lattices with implications for natural antiferromagnets as well as frustrated spin-liquid materials. [1] Farhan, A., Derlet, P.M., Kleibert, A., Balan, A., Chopdekar, R.V., Wyss, M., Anghinolfi, L., Nolting, F. and Heyderman, L.J., Nature Physics, 9 375 (2013). [2] Gliga, S., Hrkac, G., Donnelly, C., Büchi, J., Kleibert, A., Cui, J., Farhan, A., Kirk, E., Chopdekar, R.V., Masaki, Y. and Bingham, N.S., Nature materials, 16 1106 (2017). [3] Vansteenkiste, A. and Van de Wiele, B., Journal of Magnetism and Magnetic Materials, 323 2585 (2011).

Authors: Ke Liu, Jonas Greitemann, Nihal Rao, Nicolas Sadoune, Han Yan, Ludovic D. C. Jaubert, Nic Shannon, and Lode Pollet Abstract: Machine-learning techniques are efficient tools for discovering structures in high dimensional complex data and have demonstrated their power in many disciplines of physics, ranging from material science to quantum information and from high-energy physics to condensed matter physics. In this talk, we present a versatile machine-learning framework, tensorial kernel support vector machine (TK-SVM), to study many-body spin systems. This machinery is devised for exploring complex phase diagrams and characterizations of intricate phases in an unsupervised fashion, with no requirement of prior insight or particular knowledge of a system. We apply this method to investigate four highly frustrated systems: (i) an XXZ model on the pyrochlore lattice, (ii) a breathing pyrochlore magnet with Dzyaloshinskii–Moriya interaction, (iii) a honeycomb Kitaev-Gamma magnet under an external field, and (iv) an extended Heisenberg-Kitaev-Gamma magnet, containing instances where the phase diagram is well established and others where the phase diagram is not entirely resolved with other approaches. In the first example, our machine successfully identifies the distinct classical spin liquids and hidden order in the XXZ pyrochlore magnet and reproduces the associated local constraints and tensorial order parameters. In the second example, we identify the previously unknown nature of an unconventional q=W phase, coming from the ordering of a rank-2 U(1) spin liquid. In the third example, our machine detects a novel S3Z3 magnet featuring a spin-orbit entangled modulation and reveals that the origin of unconventional orders in the honeycomb Kitaev-Gamma model can be understood by the cooperation and competition between two spin liquids. In the fourth example, the machine detects another novel phase, which has a nested zigzag-stripy structure, and finds that the projection of the proximate spin-liquid material alpha-RuCl3 in the J-K-Gamma subspace lies in the frontier of several competing phases, including the modulated S3Z3 magnet, the nested zigzag-stripy magnet and a ferromagnet. The experimentally observed zigzag order is only stabilized when introducing an additional Gamma' and/or J3 exchange. Our results represent rare instances of a machine-learning method providing new physics and pave the way for developing machine learning from potential to practical research tools.

P.W. Anderson’s famous conjecture that doped quantum spin liquid (QSL) might lead to superconductivity, is one of the most important candidates for the mechanism of high-Tc superconductivity. Consequently, the spin-1/2 square-lattice J1-J2 antiferromagnetic(AFM) Heisenberg model is one of the most interesting quantum spin models, which may have QSL ground states as mother states to check this conjecture. Also as one of the most challenging spin models, the nature of the intermediate nonmagnetic phase is still under great debates, in spite of intensively studied in the past 30 years. Especially, whether the intermediate region is a QSL is currently a matter of great concern to the community. Previous methods have different conclusions due to their approxiamtions. Not to mention some biased methods, even for the unbiased DMRG method, different conclusions could be obtained. For example, an early DMRG study claimed the intermediate region is a gapped Z2 quantum spin liquid; a recent DMRG study with SU(2) symmetry proposed a plaquette valence-bond solid (VBS), while the most recent DMRG study suggests both QSL and VBS can appear in the intermediate region. The underlying reason for the differences is that DMRG is essentially a one-dimensional method and can not capture correct entanglement structure for large 2D systems. As the extensions of DMRG to higher dimensions, projected entangled pair states (PEPS) provide a powerful tool to describe 2D quantum many-body systems. However, the power of PEPS is severely hindered because of their highly non-trivial complexity. Recently, I developed an very accurate finite PEPS method, which overcomes the encountered core problems in PEPS practical applications. Applying this state-of-the-art method to the J1-J2 model up to 24x24 sites, we provide very strong evidences to show that the nonmagnetic region is mainly covered by a gapless QSL, and there also exists a narrow region for VBS phase. The critical exponents of AFM-QSL and QSL-VBS tranistions are also obtained, which point to a new universality class of quantum phase transitions that has never been observed in other models. Our results can explain the origin of different scenarios from other studies. We also give rise to the first solid PEPS calculation beyond DMRG through one-to-one direct benchmark for small system sizes. (arxiv:1908.09359 and arxiv:2009.01821)

We consider the phase diagram of a spin-1/2 J1-J2 Heisenberg model on the frustrated square-kagome geometry through a Schwinger boson analysis [1]. In this system, while asymptotic limits are reasonably well understood, the intermediate regime where the strongest competitions arise remains elusive. Here we report the presence of exotic magnetic phases obtained through our parton construction. In particular, we show the presence of a new gapped and topological quantum spin liquid with a weak lattice nematicity, characterized by non-trivial gauge invariant quantities (Wilson loops). The associated fourfold topological degeneracy is established by considering non-local winding fluxes. We also report the existence of two close yet different incommensurate orders from which our topological nematic spin liquid (TNSL) arises by quantum melting. In order to make contact with the recent synthesis of a similar square-kagome spin-1/2 compound [2], we also provide the expected experimental signatures of these phases by computing the dynamical structure factors.

We study magnetic spectrum of the easy-plane honeycomb anisotropic-exchange model, which can be related to the extended Kitaev-Heisenberg model through the axes transformation. We find signatures of strong magnon-magnon interactions in both zero-field zigzag state, and the paramagnetic polarized phase. We show that zigzag state is unstable towards magnon decays due to anisotropic terms. We also calculate both real and imaginary part of self-energy in the first order of $1/S$ approximation in the polarized state, find strong renormalization of the real part of the spectrum near the critical point, and propose a way to regularize unphysical divergences. Finally, we obtain dynamical spin structure factor at the $\Gamma$ point, compare it to ESR and Raman experiments in $\alpha$-RuCl$_3$ and show that our model has features similar to those observed experimentally, such as downward renormalization of the magnon mode due to repulsion from the two-magnon continuum and redistribution of the spectral weight from single magnon mode to the continuum. Therefore, the proposed model can be a useful tool to study anisotropic-exchange honeycomb magnets.

Thanks to the latest progress in cold-atom experiments with alkaline-earth-like atoms, such as 173-Yb, the expectations to observe the novel type of magnetism described by Heisenberg models with enlarged SU(N) symmetry in the near future have become quite high. In addition to the fully symmetric case, one can also study the situation in which the symmetry is partially broken by a magnetic field, which can be simulated by population imbalance. Here we will focus on the triangular SU(3) model in a magnetic field [1]. At the classical level, the ground state manifold presents an accidental continuous degeneracy, thus fulfilling a broad definition of frustration. We argue that at zero temperature three nontrivial phases appear below the fully saturated state thanks to the order-by-disorder mechanism, including a quantum-stabilized 2/3 magnetization plateau. The same kinds of phases are stabilized also by thermal fluctuations; quite interestingly, the low-field and high-field phases melt via an unconventional Berezinskii-Kosterlitz-Thouless transition mediated by half-quantized vortices. [1] Daisuke Yamamoto, Chihiro Suzuki, Giacomo Marmorini, Sho Okazaki and Nobuo Furukawa, PRL 125, 057204 (2020)

Artificial spin ice systems, two-dimensional arrays of interacting nanomagnets, provide a playground to directly observe competing interactions. Due to the anisotropic nature of the dipolar interactions, rotation of nanomagnets is a powerful way of tuning the interactions. In this paper, we experimentally examine the ground state transition from antiferromagnetic to ferromagnetic order triggered by this transformation. The as-grown magnetic configurations well agree with Monte Carlo simulations and ascribe a unique effective temperature independent of the rotation angle. Deviations from the theoretical ground state and behavior at transition are therefore well explained.

Geometrical frustration has led to rich insights into condensed matter physics, especially as a mechanism to produce exotic low-energy states of matter. Here we show that frustration provides a natural vehicle to generate models exhibiting anomalous thermalization of various types within high-energy states. We consider three classes of nonintegrable frustrated spin models: (I) systems with local conserved quantities where the number of symmetry sectors grows exponentially with the system size but more slowly than the Hilbert space dimension, (II) systems with exact eigenstates that are singlet coverings, and (III) flatband systems hosting magnon crystals. We argue that several one- and two-dimensional models from class I exhibit disorder-free localization in high-energy states so that information propagation is dynamically inhibited on length scales greater than a few lattice spacings. We further show that models of classes II and III exhibit quantum many-body scars: eigenstates of nonintegrable Hamiltonians with finite-energy density and anomalously low-entanglement entropy. Our results demonstrate that magnetic frustration supplies a means to systematically construct classes of nonintegrable models exhibiting anomalous thermalization in mid-spectrum states.

We combine the anisotropy of magnetic interactions and the point symmetry of finite solids in the study of dipolar clusters as new basic units for multiferroics metamaterials. The Hamiltonian of magnetic dipoles with an easy axis at the vertices of polygons and polyhedra, maps exactly into a Hamiltonian with symmetric and antisymmetric exchange couplings. The last one gives rise to a Dzyaloshinskii-Moriya contribution responsible for the magnetic modes of the systems and their symmetry groups, which coincide with those of a particle in a crystal field with spin-orbit interaction. We find that the clusters carry spin current and that they manifest the magnetoelectric effect. We expect our results to pave the way for the rational design of magnetoelectric devices at room temperature.

Motivated by the physical properties of vesignieite BaCu3V2O8(OH)2, we study the J_1-J_3 Heisenberg model on the kagome lattice, that is proposed to describe this compound for J_1<0 and J_3>>|J_1|. The nature of the classical ground state and the possible phase transitions are investigated through analytical calculations and parallel tempering Monte Carlo simulations. For large J_3, the ground states are not all related by an Hamiltonian symmetry. Order appears at low temperature via the order by disorder mechanism, favoring collinear configurations and leading to the emergence of a q=4 Potts parameter and to a finite temperature phase transition. For intermediate J_3, the ground state goes through a succession of semi-spiral states, possibly giving rise to multiple phase transitions at low temperatures. Effect of quantum fluctuations are studied through linear spin wave approximation and high temperature expansions of the $S=1/2$ model.

The spin-1 bilinear-biquadratic model has been widely used in order to describe nematic phases of matter. At a special point in the parameter space, the model is equivalent to the SU(3) Heisenberg model, which is interesting in its own right from a theoretical point of view. However, it is difficult to realize the SU(3) Heisenberg model in solid-state materials due to its high spin symmetry. Ultracold alkaline-earth(-like) atoms such as $^{173}{\rm{Yb}}$ in optical lattice provide an ideal platform for the exploration of the SU(

Structural and magnetic properties of a quasi-one-dimensional spin-$1/2$ compound NaVOPO$_4$ are explored by x-ray diffraction, magnetic susceptibility, high-field magnetization, specific heat, electron spin resonance, and $^{31}$P nuclear magnetic resonance measurements, as well as complementary \textit{ab initio} calculations. Whereas magnetic susceptibility of NaVOPO$_4$ may be compatible with the gapless uniform spin chain model, detailed examination of the crystal structure reveals a weak alternation of the exchange couplings with the alternation ratio $\alpha\simeq 0.98$ and the ensuing zero-field spin gap $\Delta_{0}/k_{\rm B} \simeq 2.4$~K directly probed by field-dependent magnetization measurements. No long-range order is observed down to 50\,mK in zero field. However, applied fields above the critical field $H_{c1}\simeq 1.6$\,T give rise to a magnetic ordering transition with the phase boundary $T_{\rm N} \propto {(H - H_{\rm c1})^{\frac{1}{\phi}}}$, where $\phi \simeq 1.8$ is close to the value expected for Bose-Einstein condensation of triplons. With its weak alternation of the exchange couplings and small spin gap, NaVOPO$_4$ lies close to the quantum critical point.

We report on our transcription of a recently developed multiloop truncation approach for electronic FRG calculations to the pseudo-fermion functional renormalization group (pf-FRG) for interacting quantum spin systems. We discuss in detail the conceptual intricacies of the flow equations generated by the multiloop truncation, as well as our essential refinements to the integration scheme for the resulting integro-differential equations. To benchmark our approach we analyze geometrically frustrated Heisenberg models on the simple cubic, face-centered cubic, and pyrochlore lattice, discussing the convergence of physical observables for higher-loop calculations and comparing with exact quantum Monte Carlo results where available. Combined, these methodological refinements systematically improve the pf-FRG approach to one of the numerical tools of choice when exploring frustrated quantum magnetism in higher spatial dimensions

We study the spin-1/2 ferromagnetic Heisenberg-Kitaev-$\Gamma$ model in the anisotropic (Toric code) limit to reveal the nature of the quantum phase transition between the gapped Z2 quantum spin liquid and a spin-ordered phase (driven by Heisenberg interactions) as well as a trivial paramagnet (driven by pseudodipolar interactions $\Gamma$). The transitions are obtained by a simultaneous condensation of the Ising electric and magnetic charges—the fractionalized excitations of the Z2 quantum spin liquid. Both these transitions can be continuous and are examples of deconfined quantum critical points. Crucial to our calculations are the symmetry implementations on the soft electric and magnetic modes that become critical. In particular, we find strong constraints on the structure of the critical theory arising from time-reversal and lattice translation symmetries with the latter acting as an anyon permutation symmetry that endows the critical theory with a manifestly self-dual structure. We find that the transition between the quantum spin liquid and the spin-ordered phase belongs to a self-dual modified Abelian Higgs field theory while that between the spin liquid and the trivial paramagnet belongs to a self-dual Z2 gauge theory. We also study the effect of an external Zeeman field to show an interesting similarity between the polarized paramagnet obtained due to the Zeeman field and the trivial paramagnet-driven pseudodipolar interactions. Interestingly, both the spin liquid and the spin-ordered phases have easily identifiable counterparts in the isotropic limit and the present calculations may shed insights into the corresponding transitions in the material relevant isotropic limit.

Motivated by the intriguing mode splittings in a magnetic field recently observed with inelastic neutron scattering in the spin ladder compound (C$_5$H$_{12}$N)$_2$CuBr$_4$ (BPCB) [1], we investigated the nature of the spin ladder excitations using density matrix renormalization group and simple analytical arguments [2]. We explore the dynamical structure factor of the frustrated ladder for different values of frustration, in which the bound states are observed close to $k=0$ above first critical field ($H_{c 1}$). We use the 2nd order perturbative expansion close to Fully Frustrated spin ladder to obtain the dispersion of boundstates and these analytical conclusions match the numerical results perfectly. We numerically demonstrate the evolution of bound states as we decrease the frustration to reach the spin ladder case. The same analysis has been extended to higher energy bound states to provide a complete understanding of the features observed in the dynamical structure factor of the frustrated and the unfrustrated spin-ladder. The bound states are characterized by a field-independent binding energy and an intensity that grows with $H-H_{c 1}$. These predictions are shown to explain quantitatively the split modes observed in BPCB. [1] Dominic Blosser, Vivek K. Bhartiya, D. J. Voneshen, Andrey Zheludev, Phys. Rev. Lett. \textbf{121} 247201 (2018) [2] Mithilesh Nayak, Dominic Blosser, Andrey Zheludev, Frédéric Mila, Phys. Rev. Lett. \textbf{124} 087203 (2020)

The Hopf insulator is an example of topological insulators with an intrinsic magnetic order [1]. Its tight-binding description can be given by the outer-orbital electrons moving in a non-collinear static magnetic background of the core electrons. Similar to the Chern insulator the Hopf insulator does not require any symmetry to possess an integer topological invariant — the Hopf invariant. In our work, we study the crystalline Hopf insulator in the presence of rotational symmetry. We show that such symmetry allows to define an additional topological invariant — a quantized difference in the electric polarization between rotation-invariant points in the Brillouin zone, which we call the returning Thouless pump. We prove using the homotopy theory that the returning Thouless pump and the Hopf invariant are not independent of each other, but must obey a relation that is given by the real-space locations of the electron orbitals. The bulk boundary correspondence of the returning Thouless pump allows to explain the surface states at sharp boundaries that were numerically observed in [1]. As these surface states are not robust under surface perturbations [2] we employ the bent Berry-Zak phase to formulate the bulk-boundary correspondence that is valid for any surface termination. [1] Moore, J. E., Ran, Y. & Wen, X.-G. Topological Surface States in Three-Dimensional Magnetic Insulators. Physical Review Letters 101, (2008). [2] Alexandradinata, A., Nelson, A. & Soluyanov, A. A. Teleportation of Berry curvature on the surface of a Hopf insulator. arXiv:1910.10717 [cond-mat] (2020).

The functional renormalization group (FRG) method has proven to be a powerful numerical tool to describe ground state properties of frustrated quantum spin systems. In its usual implementation, spin operators are expressed in terms of complex fermions, so-called pseudo-fermions. This type of representation, however, introduces unphysical states which render an application at finite temperatures inaccurate. In contrast, in the SO(3) Majorana representation of spin operators, unphysical states are absent. Motivated by the success of the pseudo-fermion FRG, we propose a new pseudo-Majorana (pm-) FRG approach to quantum spin systems which is applicable at finite temperatures. We compare our pm-FRG with exact diagonalization on small spin clusters and present further results for the $J_1$-$J_2$ Heisenberg model on the square lattice.

The excitations in spin ice systems are emergent quasiparticles, that take the form of magnetic monopoles. The behaviour of these excitations is reflected in many of the system properties, both thermodynamic properties like the specific heat and out of equilibrium properties like the susceptibility, and recent SQUID measurements have indicated that the magnetic noise in spin ice materials is directly related to the excitations. However, the measured magnetic noise exhibits anomalous power law behaviour, which remains poorly understood. In this work, we consider a nearest neighbour model of spin ice. Using a combination of Monte Carlo simulations and effective modelling, we find that the magnetic noise spectrum is directly dependent on the density and lifetimes of the quasiparticle excitations. Finally, we present numerical results which indicate that a similar relation can be found for dipolar spin ice.

Artificial Ice systems have been widely used to explore frustration, producing exciting results such as logic devices, information storage, glassy dynamics, and domain formation. But artificial ice systems are 2D which costs either the degeneracy, in the case of square ice, or the vertex neutrality in the case of the Honeycomb spin ice. That is why the recovery of degeneracy in square lattices is a long-standing challenge in the artificial spin ice community. We combine experiments, theory, and Monte Carlo simulations to demonstrate that, applying a shear transformation to the square lattice recovers partially the ground-state degeneracy, maintaining the charge neutrality of the vertices. Our method opens an avenue to engineer a novel class of frustrated micro- and nano-structures based on sheared magnetic lattices in a wide range of soft- and condensed-matter systems.

The last decades of research in frustrated magnetism have pointed out that the route to stabilize a quantum version of spin ice is to introduce transverse couplings, as opposed to Ising coupling terms. However, if too large, these transverse terms are expected to stabilize ordered phases. In this context, the question whether classical ordered phases may be stabilized out of coulombic phases via a Higgs mechanism, has become an important issue. In the present study, we tackle this question experimentally in Nd$_2$Zr$_2$O$_7$. This pyrochlore magnet is indeed an excellent candidate to explore this physics: its ground state is known to be antiferromagnetically ordered in the so-called all in -- all out (AIAO) state, but its paramagnetic phase above the ordering temperature remains enigmatic and could be a novel example of Coulomb phase, as suggested by our early experiments (Petit {\it et al.}, Nature Phys. 2016). Recently, Xu {\it et al.} (Phys. Rev. Lett. 2020) proposed that the transition from this possible Coulomb phase towards the AIAO phase could be driven by a Higgs mechanism. We have performed a careful study of the dynamics and of the magnetic correlations below and above the transition temperature ($T_{\rm N}\approx300$ mK) using high resolution inelastic and polarized neutron scattering experiments. We confirm the coulombic nature of the phase above the ordering temperature. In addition, we show that in this Coulomb phase, the spin dynamics contains features typical of the low temperature AIAO phase, i.e. a gapped spin ice-like flat mode and dispersing spin waves. This is highly unexpected and points to a competition between the high temperature Coulomb phase and the AIAO ground state. Our observations preclude the proposed Higgs mechanism, and suggest that the transition rather arises in the thermal regime of the Coulomb phase.

Dipolar-octupolar pyrochlore magnets in a strong external magnet field applied in the [110] direction are known to form a “chain” state, with subextensive degeneracy. Magnetic moments are correlated along one-dimensional chains carrying effective Ising degrees of freedom which are noninteracting on the mean-field level. Here we investigate this phenomenon in detail, including the effects of quantum fluctuations. To this end, we map out the classical ground state phase diagram of dipolar-octupolar pyrochlores in a [110] field. We identify two distinct types of chain phases, both featuring distinct subextensive, classical ground-state degeneracy. Focusing on one of the two kinds, we discuss lifting of the classical degeneracy by quantum fluctuations. We find that the energy scales on which ground-state selection occurs are small and also organised in a clear hierarchy, with the effective dimensionality of the system varying in an intricate way as the hierarchy is descended. We derive an effective two-dimensional anisotropic triangular lattice Ising model with only three free parameters which accounts for the observed behaviour. Connecting our results to experiment, they are consistent with the observation of a disordered chain state in Nd$_2$Zr$_2$O$_7$. We also show that the presence of two distinct types of chain phases has consequences for the field-induced breakdown of the apparent $U(1)$ octupolar quantum liquid phase recently observed in Ce$_2$Sn$_2$O$_7$.

In frustrated magnetic systems with competing interactions, fluctuations can lift the residual accidental degeneracy through the mechanism known as order by disorder. The state selection may have different outcomes for quantum and thermal fluctuations. As an example, we consider the semiclassical Heisenberg fcc antiferromagnet with only the nearest-neighbor interactions. Zero-point oscillations select the type 3 collinear antiferromagnetic state at $T=0$. Thermal fluctuations favor instead the type 1 antiferromagnetic structure. The opposite tendencies result in a finite-temperature transition between the two collinear states. We expand our study to the whole phase diagram of the $J_1$-$J_2$ model on the fcc lattice, which hosts a variety of ordered phases, and investigate the possibility for a quantum spin liquid phase at the critical point $J_2=\frac{1}{2}J_1$.

We present numerical evidence for the crystallization of magnons below the saturation field at non-zero temperatures for the highly frustrated spin-half kagome Heisenberg antiferromagnet. This phenomenon can be traced back to the existence of independent localized magnons or equivalently flat-band multi-magnon states. We present a loop-gas description of these localized magnons and a phase diagram of this transition, thus providing information for which magnetic fields and temperatures magnon crystallization can be observed experimentally. The emergence of a finite-temperature continuous transition to a magnon-crystal is expected to be generic for spin models in dimension D>1 where flat-band multi-magnon ground states break translational symmetry.

In this talk, I will present a study of transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu* universality classes in (2+1) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a $t$-$V$ model of spinless fermions allows us to make use of large-scale numerical results, as well as in a honeycomb-lattice model, for which we employ $\epsilon$-expansion and large-$N$ methods to estimate the critical behavior. Our results are potentially relevant for Mott insulators with $d^1$electronic configurations and strong spin-orbit coupling, or for twisted bilayer structures of Kitaev materials.

Long-range entanglement present in a Quantum spin liquid(QSL) phase of a matter allows the material to host a set of exotic excitations with fractionalised quantum numbers. Absence of conventional ordering in spite of long-range correlation and exotic properties of the excitations pose a challenge to its experimental detection. There is a growing consensus from various recent works that a promising probe to the fictionalised degrees of freedom is their coupling to the phonons. Here we present two explicit realisations of QSLs which can be probed using magnetoelastic coupling. i. S = 1/2 honeycomb iridate Cu$_2$IrO$_3$, a candidate Kitaev QSL with fractionalised Majorana fermions and Ising gauge excitations. ii. S = 1/2 rare-earth pyrochlore Pr$_2$Zr$_2$O$_7$, a candidate non-Kramers U(1) QSL with gapless linearly dispersing photon-like excitations and gapped monopole degrees of freedom which carry U(1) charge. In both cases, the signature of the magnetoelastic coupling can be observed via Raman scattering experiment. In the case of Cu$_2$IrO$_3$, Raman experiment shows promising results of anomalous broadening of the linewidth of the intensity peaks and frequency softening of the phonons. We theoretically derive this low-temperature anomalous behaviour by calculating the dressed self-energy of the phonon in presence of magnetoelastic coupling. In the case of Pr$_2$Zr$_2$O$_7$, we point out that an unusual spin-phonon coupling is present which is linear in both spin and phonon in addition to the natural coupling which is quadratic in spin. This additional feature is shown to be a consequence of the non-Kramers nature of the low energy crystal field doublet. In this case also, the broadening of the Raman linewidth is naturally ascribed to the new scattering channels with phonons decaying into emergent monopole excitations of the U(1) QSL.

We study the classical Heisenberg model on the geometrically frustrated Shastry-Sutherland (SS) lattice with additional Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field. We show that several noncollinear and noncoplanar magnetic phases, such as the flux, all-in/all-out, 3-in–1-out/3-out–1-in, and canted-flux phases are stabilized over wide ranges of parameters in the presence of the DM interaction. We discuss the role of DM interaction in stabilizing these complex magnetic phases. When coupled to these noncoplanar magnetic phases, itinerant electrons experience a finite Berry phase, which manifests in the form of topological Hall effect, whereby a nonzero transverse conductivity is observed even in the absence of a magnetic field. We study this anomalous magneto-transport by calculating the electron band structure and transverse conductivity for a wide range of parameter values, and demonstrate the existence of topological Hall effect in the SS lattice. We explore the role of the strength of itinerant electron-local moment coupling on electron transport and show that the topological Hall features evolve significantly from strong to intermediate values of the coupling strength, and are accompanied by the appearance of a finite spin Hall conductivity.

Magnetic ions positioned on a hyper-kagome lattice is a frustrated arrangement, which can lead to unconventional magnetic states including a spin liquid. Of particular interest are systems where the ions on such a lattice exhibit strong spin-orbit coupling. A decade ago the first realization of such a system was discovered in the form of Na$_4$Ir$_3$O$_8$ [1], which is an insulator and was found to exhibit spin freezing at $\approx$ 7 K [2,3]. Since then, a related system has been synthesized - Na$_3$Ir$_3$O$_8$ which has a different crystal structure, but the underlying hyperkagome arrangement of iridium ions is preserved [4]. Moreover, the iridium valence in this system is 4.33+ and not 4+ like in the parent compound. Therefore, it can be seen as a 1/3 hole doped hyper-kagome spin system. Due to a complex interplay between inter-site hopping, Coulomb repulsion, crystal field splitting and spin-orbit coupling, it is a semi-metal. In this contribution, we present a microscopic study of the Na$_3$Ir$_3$O$_8$ compound by using $^{23}$Na NMR. We determine the intrinsic behavior of the uniform \textbf{q} $ = 0$ susceptibility via shift measurements and the dynamical response by probing the spin-lattice relaxation rate. Throughout the studied temperature range, the susceptibility is consistent with a semimetal behavior, though with electronic bands substantially modified by correlations. Remarkably, the antiferromagnetic fluctuations present in the insulating parent compound Na$_4$Ir$_3$O$_8$ survive in the studied compound. The spin dynamics are consistent with 120$^o$ excitations modes displaying short-range correlations [5]. \vspace{0.5 cm} [1] Y. Okamoto \textit{et al}, Phys. Rev. Lett. {\bf 99}, 137207 (2007) [2] R. Dally \textit{et al}, Phys. Rev. Lett. {\bf 113}, 247601 (2014) [3] A. C.~Shockley \textit{et al}, Phys. Rev. Lett. {\bf 99}, 047201 (2015) [4] T. Takayama \textit{et al}, Scientific Reports {\bf 4}, 6818 (2014) [5] G. Simutis \textit{et al}, arXiv:2007.01633 (2020)

Co$^{2+}$ ions in an octahedral crystal field, stabilise a j$_{eff}$ = 1/2 ground state with an orbital degree of freedom and have been recently put forward for realising Kitaev interactions, a prediction we have tested by investigating spin dynamics in two cobalt honeycomb lattice compounds, Na$_2$Co$_2$TeO$_6$ and Na$_3$ Co$_2$SbO$_6$, using inelastic neutron scattering. We used linear spin wave theory to show that the magnetic spectra can be reproduced with a spin Hamiltonian including a dominant Kitaev nearest-neighbour interaction, weaker Heisenberg interactions up to the third neighbour and bond- dependent off-diagonal exchange interactions. Beyond the Kitaev interaction that alone would induce a quantum spin liquid state, the presence of these additional couplings is responsible for the zigzag-type long-range magnetic ordering observed at low temperature in both compounds. These results provide evidence for the realization of Kitaev-type coupling in cobalt-based materials, despite hosting a weaker spin-orbit coupling than their 4d and 5d counterparts.

Various artificial magnetic nanostructures can be constructed due to the advances in electron beam lithography. Following the roadmap provided by Morrison et al. [NJP 15, 045009 (2013)] new magnetic nanostructures can be created out of square artificial spin ice lattices by removing and merging of magnetic elements. Here we present one of such structures, composed of elements with two different sizes and therefore two activation energies for the interacting nano-magnetic elements. With statistical analysis of synchrotron-based magnetic microscopy we can show that the two energy-scales in this lattice have no measurable impact on the magnetic ordering in the short-range order, as we compare the lattice with a reference lattice only composed of one element size. But investigating flux-closure loops and the ground state manifold in this lattice provides us strong evidence for intermediate range interaction and ordering promoted by the two energy-scales. These results are necessary to understand the impact of different element sizes and energy-scales in artificial magnetic nanostructures and therefore needed to tailor the magnetic ordering in magnetic nanostructures and beyond.

We investigate the ground-state phase diagram of the $S=1/2$ Kitaev-Heisenberg-$\Gamma$ model on the honeycomb lattice by several numerical methods including dimer series expansion, exact diagonalization, and density-matrix-renormalization-group. In this study, we focus on the effects of the anisotropic interaction that changes the system from the isolated dimer model to the spin-chain model by tuning the coupling constants. We find that, in the spin-chain limit, a Tomonaga-Luttinger liquid is stable even when SU(2) symmetry is absent and otherwise, magnetically long-range-ordered states appears. All of the long-range-ordered states become two-dimensional long-range ordered states by the infinitesimal interchain interaction. Starting from the isolated dimer limit, a triplet dimer phase survives up to the isotopically interacting system in a large part of the phase diagram, where the off-diagonal symmetric ($\Gamma$) interactions are ferromagnetic and the Kitaev or Heisenberg interactions are antiferromagnetic. Otherwise, a phase transition to a magnetically ordered phase occurs before the interaction becomes isotopic. This indicates that the quantum spin liquid proposed in the $\Gamma$ model is unstable against the anisotropy of the interactions.

Interaction and disorder are the corner stones of quantum condensed matter physics, with lattice frustration bringing in the third dimension to this scenario. The interplay between these competing phenomena is once again in the forefront owing to the recent interest on two-dimensional frustrated materials such as, transition metal dichalcogenides (TMD). We report the first theoretical investigation of this interplay, carried out using a non perturbative Monte Carlo simulation. Based on the spectroscopic and transport signatures, we map out the phase diagram of the Anderson-Hubbard model for a triangular lattice. Our results show that the interplay of disorder and frustration aids in to stabilize a metallic phase with underlying magnetic order, over a regime of intermediate disorder strength. As the function of increasing disorder the system thus undergoes a Mott insulator-antiferromagnetic metal-Anderson insulator transition. At finite temperatures the interplay between the disorder induced randomness and fluctuating magnetic moments give rise to non trivial spectroscopic and transport signatures, suggestive of a pseudogap metallic phase. Being the first of its kind our work sets up the theoretical framework and opens up avenues for understanding the experimental observations of systems where disorder, interaction and lattice frustration compete with each other.

Deconfined quantum criticality (DQC) predicts a generic continuous quantum phase transition between a 2+1d Néel antiferromagnetic phase and a valence-bond solid (VBS) phase. Since the two most basic antiferromagnetic phases spontaneously break totally different symmetries, the standard Ginzburg-Landau framework would expect a first-order transition. The DQC scenario thus suggests a deeper connection between them. From its original proposal, DQC has been a concept difficult to concretely realize in a microscopically defined Hamiltonian. While the discovery of the JQ model amenable to quantum Monte Carlo (QMC) method led to high-precision numerics of the DQC point consistent with a continuous transition [1], there still remained some puzzling aspects, such as anomalous finite size scaling and inconsistency with conformal bootstrap bounds. In this presentation, I will show two new phases that we found in our recent studies of variants of the JQ model, possibly explaining such oddities. Although the original DQC scenario argued that columnar and plaquette VBS would both have similar properties in the context, the original JQ model only realized a Néel-to-columnar VBS transition. We construct a new JQ-like model that now has a Néel-to-plaquette VBS transition, and observe a striking first-order transition with emergent SO(5) symmetry [2] never observed before. We also find a relevant field for the DQC point, revealing that the conventional DQC point is actually a "tip of an iceberg" where two different phase transitions are simultaneously taking place [3], explaining the anomalous scaling behaviors. [1] H. Shao, W. Guo, and A. W. Sandvik, Science 352, 213 (2016) [2] J. Takahashi and A. W. Sandvik, Phys. Rev. Research 2, 033459 (2020) [3] B. Zhao, J. Takahashi, and A. W. Sandvik, arXiv:2005.10184 (2020) (accepted to PRL)

Quantum fluctuation and frustration lead to a new phase of matter, a quantum spin liquid (QSL), where spins do not have long-range order in the zero-temperature limit. The Kitaev model, an exactly solvable model on the honeycomb plane realizes a frustrated spin system with the bond-dependent Ising interactions. Since Jackeli and Khaliullin discovered that such interactions arise in the honeycomb layered materials, the model has been discussed from both the theoretical and experimental points of view. $\alpha$-RuCl$_3$ under an applied strong magnetic field is one of the best candidates for the Kitaev model. In this setup, Y. Kasahara et al. reported direct evidence of Majorana fermions via the half-integer thermal quantum Hall effect. They also mentioned the disappearance of the half-integer thermal quantum Hall effect at higher fields. Moreover, in recent experiments by O. Tanaka et al., it is reported that the three-fold rotational symmetry is broken at high fields in the bulk and that it seems there is a nematic phase transition in which the half-integer thermal quantum Hall effect disappears. These fascinating phenomena lead us to consider four-body interactions among Majorana particles, and we added this new term to the pure Kitaev model with an external magnetic field. We evaluated its effect by using the mean-field theory and also employed the exact diagonalization to confirm the results of the mean-field calculation. We found that a drastic phase transition occurs due to the four-Majorana interactions under applied magnetic fields. A topological phase transition which can be described by the change of the Chern number occurs simultaneously as a nematic phase transition that breaks the rotational symmetry of the system. Thus, we call this transition topological nematic phase transition and we also figured out that this exotic transition is classified in the first-order transition.

Recently, Li and Franz introduced an interacting Majorana model on the honeycomb lattice [PRB 98, 115123 (2018)], where the strong interaction limit was advocated to harbour a highly-entangled spin liquid ground state. In our work, we reveal an intricate algebraic structure in the eigenvalue spectrum despite the model being non-integrable. We discuss the impact of our results on the way towards a deeper understanding of the nature of this peculiar quantum spin liquid.

The three-dimensional quenched random bond diluted $(J_1-J_2)$ quantum Heisenberg antiferromagnet is studied on a simple-cubic lattice. Using extensive stochastic series expansion quantum Monte Carlo simulations, we perform very long runs for $L \times L \times L$ lattice up to $L=48$. By employing standard finite-size scaling method, the numerical values of the N\'eel temperature are determined with high precision as a function of the coupling ratio $r=J_2/J_1$. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical $3D$ $O(3)$ Heisenberg universality class.

Complex magnetic orders in frustrated magnets may exhibit rich melting processes when the magnet is heated toward the paramagnetic phase. We show that one may tune such melting processes by quantum fluctuations. We consider a kagome lattice dipolar Ising model subject to transverse field and focus on the thermal transitions out of its magnetic ground state, which features a root 3 by root 3 magnetic unit cell. Our quantum Monte Carlo (QMC) simulations suggest that, at weak transverse field, the root 3 by root 3 phase melts by way of an intermediate magnetic charge ordered phase where the lattice translation symmetry is restored while the time reversal symmetry remains broken. By contrast, at stronger transverse field, QMC simulations suggest the root3 by root3 order melts through a floating Kosterlitz-Thouless phase. The two distinct melting processes are separated by either a multicritical point or a short line of first order phase transition.

Frustration in quantum magnets gives rise to many complex phase diagrams and phenomena. Yet, especially in higher dimensions, their unbiased treatment still poses a challenge. In the case of quantum Monte Carlo methods, such as the stochastic series expansion (SSE), large-scale simulations are hindered by the negative sign problem. Usually present in the face of geometric frustration, it can in principle be avoided by a change of basis. However, such sign-free bases are only known for a set of special models. In this work, we extend this set to lattices comprised of fully-frustrated spin trimers. Using the SSE, we simulate two different spin-trimer models and investigate the role of the spin-chirality degree of freedom internal to each constituent trimer. For the square lattice of triangles, we refute earlier claims of chirality order, whereas in the fully-frustrated trilayer limit, the chirality induces a macroscopic jump in the entropy at a quantum first-order phase transition. These results advance the understanding of frustrated models with multicomponent local Hilbert spaces and increase the applicability of Monte Carlo methods in these systems.

The search for valence-bond-solid (VBS) phases in 2D antiferromagnets (AFMs) has attracted a lot of interest due to the proposal of a continuous deconfined quantum phase transition that is beyond the Landau-Ginzburg-Wilson paradigm. While VBS order often appears in frustrated spin systems, large-scale quantum Monte Carlo studies have mainly concentrated on a class of designer Hamiltonians called J-Q models that can be simulated without a sign problem. It is of current interest to find VBS order also in more realistic models. In 1D, a coupling to phonons naturally leads to a dimerization via the spin-Peierls instability, but it is still an open question whether this is also the case in 2D. Here, we use a recently developed quantum Monte Carlo method for retarded interactions to show that a VBS state with Kekule pattern can arise in a spin-Peierls model on the honeycomb lattice. While the AFM—VBS transition is clearly first order for low phonon frequencies, it is tuned towards weakly first-order with increasing quantum lattice fluctuations. Our study reveals that retardation effects have a significant impact on the AFM—VBS transition. Moreover, we discuss relations to frustrated spin models as well as Dirac systems.

We examine the ground state phase diagram of the K-$\Gamma$ model on a honeycomb lattice using cluster expansions and numerical exact diagonalizations. Starting from the dimers on the specific bond, we strengthen the interdimer interaction to the isotropically interacting system. We find that when the $\Gamma$ interaction is positive and strong, the dimer state remains up to the isotropically interacting system, where a phase transition takes place [1]. This implies that a spin liquid argued in the $\Gamma$ model [2] is unstable against the anisotropy of the interaction. The results obtained indicate that the $C_{3v}$ symmetric Kekul$\'{e}$ dimerized state shows a phase transition before the system approaches the isotropically interacting system [1]. [1] T. Yamada, T. Suzuki, and S.-I. Suga, Phys. Rev. B 102, 024415 (2020). [2] A. Catuneanu, Y. Yamaji, G. Wachtel, Y.-B. Kim, and H.-Y. Kee, npj Quantum Materials 3, 23 (2018).

The spin-1/2 Heisenberg kagome antiferromagnet is one of the paradigmatic playgrounds for frustrated quantum magnetism, with an extensive number of competing resonating valence bond (RVB) states emerging at low energies, including gapped and gapless spin liquids and valence bond crystals. Here we revisit the crossover from this quantum RVB phase to a semiclassical regime brought about by anisotropic Kitaev interactions, and focus on the precise mechanisms underpinning this crossover. To this end, we introduce a simple parametrization of the classical ground states (GSs) in terms of emergent Ising-like variables, and use this parametrizaton: i) to construct an effective low-energy description of the order-by-disorder mechanism operating in a large part of the phase diagram, and ii) to contrast, side by side, exact diagonalization data obtained from the full basis with that obtained from the restricted (orthonormalized) basis of classical GSs. The results reveal that fluctuation corrections from states outside the restricted basis are strongly quenched inside the semiclassical regime (due to the large anisotropy spin gaps), and that the RVB phase survives up to a relatively large value of Kitaev anisotropy K. We further find that the pure Kitaev model admits a subextensive number of one-dimensional symmetries, which explains naturally the absence of classical and quantum order by disorder reported previously.

We introduce the notion of combinatorial gauge symmetry --- a local gauge transformation that includes single spin rotations plus permutation of spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated with the automorphism of these matrices with respect to monomial transformations. Based on this notion, we demonstrate how to build quantum spin liquids with physically accessible interactions.

Spiral spin liquids are unique classical spin liquids that occur in many frustrated spin systems, but do not comprise a new phase of matter. Owing to extensive classical ground-state degeneracy, the spins in a spiral spin liquid thermally fluctuate cooperatively from a collection of spiral configurations at low temperatures. These spiral propagation wavevectors form a continuous manifold in reciprocal space, i.e., a spiral contour or a spiral surface, that strongly governs the low-temperature thermal fluctuations and magnetic physics. In this paper, the relevant spin models conveying the spiral spin liquid physics are systematically explored and the geometric origin of the spiral manifold is clarified in the model construction. The spiral spin liquids based on the dimension and the codimension of the spiral manifold are further clarified. For each class, the physical properties are studied both generally and for specific examples. The results are relevant to a wide range of frustrated magnets. A survey of materials is given and future experiments are suggested.

We study the effect of Dzyaloshinskii-Moriya (DM) interaction on the triangular lattice U(1) QSL which is stabilized by ring-exchange interactions. A weak DM interaction introduces a staggered flux to the U(1) QSL state and changes the density of states (DOS) at the spinon fermi surface. If the DM vector contains in-plane components, then the spions gain nonzero Berry phase. The resultant thermal conductances $κ_{xx}$ and $κ_{xy}$ qualitatively agree with the experimental results on the material $EtMe3Sb[Pd(dmit)2]2$. Furthermore, owing to perfect nesting of the fermi surface, a spin density wave with 120◦ order is triggered by larger DM interactions. On the other hand, when the ring-exchange interaction decreases, another 120◦ ordered phase shows up which is proximate to a U(1) Dirac QSL. Although having the same pattern of magnetic order, the two AFM phases can be distinguished by their different excitation spectrum.

We study a Kitaev honeycomb model in a skew magnetic field subject to a quantum quench from a fully polarized initial product state and observe nonergodic dynamics as a consequence of disorder-free localization. We find that the system exhibits a subballistic power-law entanglement growth and quantum correlation spreading, which is otherwise typically associated with thermalizing systems. In the asymptotic steady state the Kitaev model develops volume-law entanglement and power-law decaying dimer quantum correlations even at a finite energy density. The results are robust against perturbative solvability-breaking interactions according to our numerical calculation. Above all, our work sheds light onto the potential of disorder-free localization mechanism in breaking ergodicity and allowing for nontrivial quantum state in generic Kitaev spin liquid at finite energy density.