Korrelationstage 2023

Heterogeneous electron and spin models played important rule in understanding fundamental physical systems such as Kondo and heavy fermion systems. We introduce alternating odd-even ladders where the number of sites per rung alternates between two and three~[1]. Firstly, we discuss bipartite alternating ladders modeled with the Hubbard Hamiltonian. Such ladders are amenable to the numerical methods of quasi one dimensional methods. We discuss the existence ferrimagnetic long range order arising due the difference in the number of sites between each sublattice. We provide detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. We discuss how the alternation between quasi-long-range order in uniform odd-leg ladders and spin liquid behavior in uniform even-leg ladders might be affected by a regular alternation pattern. Moreover, we restrict to ladders with equal number of sites in each sublattice but modeled with the Su-Schrieffer-Heeger (SSH) Hamiltonian. Such ladders belong to the BDI topological insulators and revealed rich topological phase diagram that depend on the choice of the unit cell. We discuss the difference between uniform two and three leg SSH ladders and the alternating SSH ladders. We provide possible connection to the difference between uniform and mixed spin chains or ladders. \vspace{5mm} \noindent [1] Magnetic properties of alternating Hubbard ladder, Phys. Rev. B, 103, 165127 (2021)

Heterogeneous electron and spin models played important rule in understanding fundamental physical systems such as Kondo and heavy fermion systems. We introduce heterogeneous (asymmetric) Hubbard ladders in which we allow different intra-leg hopping and interaction in each leg~[1,2,3]. We discuss conditions of observing properties of Luttinger liquid, Kondo-Mott insulator, Mott insulator and correlated band insulator. We discuss the enhancement of pairing binding energy and correlation in parameter regimes in the crossover between charge-transfer and Mott insulators. Our results show that pairing can not be explained by "spin singlets removal". We put in question the sufficiency/adequacy of the reduction of the three band Emery model into the single band Hubbard model to describe the pairing mechanism in cuprates. \vspace{5mm} \noindent [1] Ground-state and spectral properties of an asymmetric Hubbard ladder, Phys. Rev. B 91, 155119 (2015). \noindent [2] Correlations and confinement of excitations in an asymmetric Hubbard ladde, Eur. Phys. J. B 91, 207 (2018). \noindent [3] Pair binding and enhancement of pairing correlations in asymmetric Hubbard ladders, Phys. Rev. B,107, 125117 (2023).

The algorithms for lattice fermions library is a very general implementation of the auxiliary field quantum Monte Carlo algorithm. The poster will provide a succinct summary of possible applications including heavy fermion materials, Dirac systems, electron-phonon problems, frustrated spin systems, as well as lattice gauge theories. For further information, please visit the website, https://alf.physik.uni-wuerzburg.de.

The superconducting diode effect refers to an asymmetry in the critical supercurrent $J_c(\hat{n})$ along opposite directions, $J_c(\hat{n})\neq J_c(-\hat{n})$. While the basic symmetry requirements for this effect are known, it is, for junction-free systems, difficult to capture within current theoretical models the large current asymmetries $J_c(\hat{n})/J_c(-\hat{n})$ recently observed in experiment. We here propose and develop a theory for an enhancement mechanism of the diode effect arising from spontaneous symmetry breaking. We show---both within a phenomenological and a microscopic theory---that there is a coupling of the supercurrent and the underlying symmetry-breaking order parameter. This coupling can enhance the current asymmetry significantly. Our work might not only provide a possible explanation for recent experiments on trilayer graphene but also pave the way for future realizations of the superconducting diode effect with large current asymmetries.

We study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasifree and quadratic, respectively. We find that steady states of one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green's functions. For the quasifree case without quadratic Lindblad operators, we show that fermionic systems with finite-range interactions are noncritical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasifree bosonic systems can be critical in D>1 dimensions. Last, we address the question of phase transitions in quadratic systems and find that, without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase. References: * Y. Zhang and T. Barthel, Criticality and phase classification for quadratic open quantum many-body systems, Phys. Rev. Lett. 129, 120401 (2022). * T. Barthel and Y. Zhang, Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems, J. Stat. Mech. 113101 (2022). * T. Barthel and Y. Zhang, Superoperator structures and no-go theorems for dissipative quantum phase transitions, Phys. Rev. A 105, 052224 (2022).

When a mobile hole is doped into an antiferromagnet, its movement will distort the surrounding magnetic order and yield a magnetic polaron. The resulting complex interplay of spin and charge degrees of freedom gives rise to very rich physics and is widely believed to be at the heart of high-temperature superconductivity in cuprates. In this work, we develop from first principle a new theoretical framework to describe magnetic polarons based on recent insights on their microscopic structure and derive an effective coupling between the polaron and collective spin-wave excitations. To this end, we start from a single hole doped into an AFM described by a geometric string of displaced spins and will then introduce magnon excitations through a generalized 1/S expansion to arrive at an effective Hamiltonian. After making a Born-Oppenheimer-type approximation, this system is solved using the self-consistent Born approximation to extract the renormalized polaron properties, like its dispersion relation and the single-particle spectrum.

Kitaev exchange, a new paradigm in quantum magnetism research, occurs for 90$^{\circ}$ metal-ligand-metal links, $t_{2g}^5$ ions, and sizable spin-orbit coupling. It is being studied in honeycomb compounds but also on triangular lattices. While for the former it is known by now that the Kitaev intersite interactions are ferromagnetic, for the latter the situation is unclear. \\ Here we determine the effective coupling constants in the $t_{2g}^5$ triangular-lattice material NaRuO$_2$, recently found to host a spin-liquid phase. We show that, compared to honeycomb compounds, the characteristic triangular-lattice cation surroundings dramatically affect exchange paths and coupling parameters, changing the Kitaev interactions to antiferromagnetic. The quantum chemical analysis and subsequent effective spin model computations provide perspective onto the nature of the experimentally observed spin liquid -- it seemingly implies finite longer-range exchange, and the atypical proximity to ferromagnetic order is related to sizable ferromagnetic Heisenberg nearest-neighbor couplings [1]. \\ Additionally, we nail down the different exchange contributions to the effective magnetic couplings, in both NaRuO$_2$ and in a recently discovered high-symmetry phase of $\alpha$-RuCl$_3$ under pressure. We show that anisotropic Coulomb exchange defines a major interaction scale -- for close to ideal $j_{\mathrm{eff}}\!=\!1/2$ moments in $\alpha$-RuCl$_3$ under pressure, $\sim$45\% of the Kitaev coupling $K$ and $\sim$90\% of the off-diagonal $\Gamma^{\prime}$ [2]. Anisotropic Coulomb exchange being ignored so far in Kitaev quantum magnetism research, our analysis opens interesting new perspectives in this field. We also find a vanishingly small Heisenberg $J$ in $\alpha$-RuCl$_3$ under pressure, which yields a $K/J$ ratio $\gtrsim$100 and higher chances of materializing a Kitaev spin-orbital liquid. \vspace{2cm} [1] Pritam Bhattacharyya, Nikolay A. Bogdanov, Satoshi Nishimoto, et al. \textit{arXiv:}2212.09365 [2] Pritam Bhattacharyya, Liviu Hozoi, Quirin Stahl, et al. \textit{arXiv:}2302.00540

Confinement of excitations is usually considered as a phenomenon of high-energy physics. However, over the recent years, related effects have been discussed in condensed matter settings as well. A paradigmatic example is the formation of mesonic bound states in spin chains with linear confinement between domain walls. A prominent candidate material is the quasi-one dimensional Ising magnet $CoNb_2O_6$ for which mesonic bound states have been detected by neutron scattering experiments. In this work, we study the Raman response of a twisted Kitaev chain in the presence of a magnetic field as a minimal model for confinement in $CoNb_2O_6$ and compute the response within the theory by Fleury and Loudon. We show that the bound states directly manifest themselves as sharp peaks in the Raman response, which we numerically compute using Matrix Product States. We find that the main features of the spectrum can be well understood by a trial wave-function, which contains a few solitonic excitations only. Moreover, when approaching the critical regime Raman spectroscopy can be used to directly detect Ising quantum criticality via the emergence of the famous E8 symmetry in the response spectrum.

We investigate topological superconductivity in the Rashba-Hubbard model, describing heavy-atom superlattice and van der Waals materials with broken inversion. We focus in particular on fillings close to the van Hove singularities, where a large density of states enhances the superconducting transition temperature. To determine the topology of the superconducting gaps and to analyze the stability of their surface states in the presence of disorder and residual interactions, we develop an fRG+MFT approach, which combines the unbiased functional renormalization group (fRG) with a real-space mean-field theory (MFT). Our approach uncovers a cascade of topological superconducting states, including A1 and B1 pairings, whose wave functions are of dominant p- and d-wave character, respectively, as well as a time-reversal breaking A1+iB1 pairing. While the A1 and B1 states have first order topology with helical and flat-band Majorana states, respectively, the A1+iB1 pairing exhibits second-order topology with Majorana corner modes. Implications for experimental systems and potential applications for quantum technologies are being discussed.

The normal-state transport properties of superconducting infinite-layer nickelates are investigated within an interacting three-orbital model. It includes effective Ni-$d_{z^2}$, Ni-$d_{x^2-y^2}$ bands as well as the self-doping band degree of freedom. Thermopower, Hall coefficient and optical conductivity are modelled within a quasiparticle approximation to the electronic states. Qualitative agreement in comparison to experimentally available Hall data is achieved, with notably a temperature-dependent sign change of the Hall coefficient for larger hole doping $x$. The Seebeck coefficient changes from negative to positive in a non-trivial way with $x$, but generally shows only modest temperature dependence. The optical conductivity shows a pronounced Drude response and a prominent peak structure at higher frequencies due to interband transitions. While the quasiparticle picture is surely approximative to low-valence nickelates, it provides enlightening insights into the multiorbital nature of these challenging systems.

Weakly first-order transitions, i.e. discontinuous phase transitions with very large correlation lengths, have become a vivid subject in condensed matter research and beyond in recent years. Therefore, establishing quantum systems in which weakly first-order phase transitions can be robustly demonstrated is of great interest. We present a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions within a universal loop model formulation, combined with large-scale quantum Monte Carlo calculations. In contrast to earlier claims, the thermal melting of the nematic state is not continuous, instead we identify a weakly first-order transition. Furthermore, we obtain exact results for the order parameter distribution and cumulant ratios at the melting transition. Our findings establish the thermal melting of planar spin-nematic states as a generic platform for quantitative approaches to weakly first-order phase transitions in quantum systems with a continuous SU(2) internal symmetry.

Magnon transport in graphene quantum Hall heterojunctions has been a remarkable recent experimental development to identify spin structure of ground states at various Landau level fillings. Inspired by experiment, we introduce a theoretical model to study magnon scattering in skyrmion crystals, sandwiched between quantum Hall ferromagnets which act as the source and sink of magnons. Skyrmions are topological objects while skyrmion crystals break internal and translational symmetries, thus our setup allows us to study the interplay of topology and symmetry breaking. Starting from a basis of holomorphic theta functions, we construct an analytical ansatz for such a junction with finite spatially modulating topological charge density in the central region and vanishing in the leads. Using analytical techniques, field theory, heuristic models and microscopic recursive transfer-matrix numerics, we calculate the spectra and magnon transmission properties of the skyrmion crystal. We find that magnon transmission can be understood via a combination of low-energy Goldstone modes and effective emergent Landau levels at higher energies. The former manifests in discrete low-energy peaks in the transmission spectrum which reflect the nature of the Goldstone modes arising from symmetry breaking. The latter, which reflect the topology, lead to band-like transmission features, from the structure of which further details of the excitation spectrum of the skyrmion crystal can be inferred. Such characteristic transmission features are absent in competing phases of the quantum Hall phase diagram, and hence provide direct signatures of skyrmion crystal phases and their spectra [1]. Our results directly apply to quantum Hall heterojunction experiments in monolayer graphene with the central region doped slightly away from unit filling, and are also relevant to junctions formed by metallic magnets or in junctions with artificial gauge fields. Besides, purely SU(2) spin skyrmion crystals, we also study crystals of SU(4) entanglement skyrmions [2], in which the spin and valley degrees of freedom are entangled. We show how non-local transport signatures of magnons in such junction experiments can detect and quantify this entanglement [3], thereby establishing magnon transport as a concrete route to probe such entanglement in multicomponent quantum Hall systems. [1] Nilotpal Chakraborty, Roderich Moessner, and Benoit Doucot. “Riemann meets Goldstone: magnon scattering off quantum Hall skyrmion crystals probes interplay of symmetry break- ing and topology”: arXiv:2304.13049 (2023). [2] Benoit Doucot et al. “Entanglement skyrmions in multicomponent quantum Hall systems”. In: PRB 78, 195327 (2008) [3] Nilotpal Chakraborty, Roderich Moessner, and Benoit Doucot: In Prep

The breakdown of the lattice Kondo effect in local-moment metals can lead to non-trivial forms of quantum criticality and a variety of non-Fermi-liquid phases. Given indications that Kondo-breakdown transitions involve criticality not only in the spin but also in the charge sector, we investigate the interplay of Kondo breakdown and strong valence fluctuations in generalized Anderson lattice models. We employ a parton mean-field theory to describe the transitions between deconfined fractionalized Fermi liquids and various confined phases. We find that rapid valence changes near Kondo breakdown can render the quantum transition first order. This leads to phase-separation tendencies which, upon inclusion of longer-range Coulomb interactions, will produce intrinsically inhomogeneous states near Kondo-breakdown transitions. We connect our findings to unsolved aspects of experimental data.

We present the dynamical spin structure factor of the antiferromagnetic spin-$\frac{1}{2}$ $J_1 − J_2$ Heisenberg model on a triangular lattice obtained from large-scale matrix-product state simulations. The high frustration due to the combination of antiferromagnetic nearest and next-to-nearest neighbour interactions yields a rich phase diagram. We resolve the low-energy excitations in the $120^\circ$-ordered phase, in the putative spin liquid phase at $\frac{J_2}{J_1} = 0.125$ and in the stripe-ordered phase. In the $120^\circ$-ordered phase, we observe an avoided decay of the lowest magnon-branch, demonstrating the robustness of this phenomenon in the presence of gapless excitations. Our findings in the spin-liquid phase chime with the field-theoretical predictions for a gapless Dirac spin liquid, in particular the picture of low-lying monopole excitations at the corners of the Brillouin zone. Finally, we compare the spectral response in the stripe phase to predictions of spin-wave theory. We comment on possible practical difficulties of distinguishing proximate liquid and solid phases based on the dynamical structure factor.

Anisotropic magnetic materials may host exotic quantum excitations. Specifically, we consider the case of a strong single-ion anisotropy of the easy-axis type that may lead to unconventional collective excitations. In a lattice of spins S, this family corresponds to quasi-particles carrying $\Delta S^z=\pm2S$, labeled as longitudinal magnons. Their recent observation in S=2 van der Waals magnets FePS3 and FePSe3 raised a need for their theoretical description including the multipolar states they may generate in a strong magnetic field. Accordingly, we first developed a theory to describe these excitations in a S=1 square-lattice antiferromagnet. Using an effective model in the strong coupling regime, we derived the ground-state energy and the spectra of longitudinal magnons to leading order in perturbation theory. The results were pushed an order further by linked cluster series expansion. By contrast, the intermediate regime was described via multi-boson spin-wave theory. With regard to energy gaps in the case of a small exchange, this framework proved consistent with harmonic spin-wave theory for transverse magnons and equally with the perturbative approach for longitudinal magnons. Second, on a realistic honeycomb-lattice with a zigzag structure under significant single-ion anisotropy, we derived conditions on the exchange constants such that longitudinal magnons can be dispersive.

Electrons residing on frustrated lattices offer a fertile ground for the discovery of unprecedented solid-state phenomena, particularly in the realm of collective states of interacting electrons. This contribution highlights three intriguing cases: RuCl3, IrTe2, and CsV3Sb5, where electrons intricately couple with the lattice. By leveraging advanced X-ray diffraction techniques, we investigate the lattice structure and electronic instabilities of these materials under hydrostatic and, in one case, biaxial pressure. Through a synergistic combination of cutting-edge structure determination methods and theoretical modeling, we gain valuable new insights into the underlying interactions that govern the collective electronic behavior in these systems.

Motivated by the report of superconductivity in bilayer La$_3$Ni$_2$O$_7$ at high pressure, we examine the interacting electrons in this system. First-principles many-body theory is utilized to study the normal-state electronic properties. Below 100\,K, a multi-orbital non-Fermi liquid state resulting from loss of Ni-ligand coherence within a flat-band dominated low-energy landscape is uncovered. The incoherent low-temperature Fermi surface displays strong mixing between Ni-$d_{z^2}$ and Ni-$d_{x^2-y^2}$ orbital character. In a model-Hamiltonian picture, spin fluctuations originating mostly from the Ni-$d_{z^2}$ orbital give rise to strong tendencies towards a superconducting instability with $d_{x^2-y^2}$ order parameter. The dramatic enhancement of $T_{\rm c}$ in pressurized La$_3$Ni$_2$O$_7$ is due to stronger Ni-$d_{z^2}$ correlations compared to those in the infinite-layer nickelates.

The discovery of correlated insulating states in moir\'e heterostructures has renewed the interest in strongly-coupled electron systems where spin and valley (or layer) degrees of freedom are intertwined. In the strong-coupling limit, such systems can be effectively described by SU(4) spin-valley models akin to Kugel-Khomskii models long studied in the context of spin-orbit coupled materials. However, typical moiré heterostructures also exhibit interactions that break the SU(4) symmetry down to SU(2)$\otimes$U(1). Here we investigate the impact of such symmetry-breaking couplings on the magnetic phase diagram for triangular superlattices considering a filling of two electrons (or holes) per moiré unit cell. We explore a broad regime of couplings -- including XXZ anisotropies, Dzyaloshinskii-Moriya exchange and on-site Hund's couplings -- using semi-classical Monte Carlo simulations. We find a multitude of classically ordered phases, including (anti-)ferromagnetic, incommensurate, and stripe order, manifesting in different sectors of the spin-valley model's parameter space. Zooming in on the regimes where quantum fluctuations are likely to have an effect, we employ pseudo-fermion functional renormalization group (pf-FRG) calculations to resolve quantum disordered ground states such as spin-valley liquids, which we indeed find for certain parameter regimes. As a concrete example, we discuss the case of trilayer graphene aligned with hexagonal boron nitride using material-specific parameters.

URhGe is a ferromagnetic superconductor that exhibits exotic magnetic properties, including a metamagnetic transition and an interesting phase diagram with a tricritical point [1,2]. We investigate the metamagnetic transition observed in URhGe by studying the Heisenberg model with a complex form of anisotropy. Our calculations successfully predict the first-order transition at low temperatures and the magnitude of the jump and the critical angle, as determined by our analyze, are in agreement with experimental observations [3]. We obtain the unique T-H phase diagram using Monte Carlo simulations. We further explore the tricritical behavior in URhGe and identify the tricritical point in the T-H phase diagram. We investigate the scaling relations near the tricritical point, providing valuable insights into universality class and tricritical exponents [4]. Overall, our theoretical work provides the understanding of the metamagnetic transition and tricritical behavior in URhGe. The insights gained not only deepen our knowledge of this specific compound but also contribute to the broader understanding of magnetism in uranium superconductors. [1] D. Aoki et al., Nature (London) 413, 613 (2001). [2] F. Lévy et al., Science 309, 1343 (2005). [3] S. Nakamura et al., PRB 96, 094411 (2017). [4] H. J. Herrmann and D.P. Landau, PRB 48, 1 (1993).

The salient property of the electronic band structure of twisted bilayer graphene (TBG), at the so-called magic angle (MA), is the emergence of flat bands around the charge neutrality point. These bands are associated with the observed superconducting phases and the correlated insulating states occurring at the MA. Scanning tunneling microscopy combined with angle resolved photoemission spectroscopy are usually used to visualize the flatness of the band structure of the TGB at the MA. Here, we theoretically argue that spin pumping (SP) provides a direct probe of the flat bands of TBG and an accurate determination of the MA. We consider a junction separating a ferromagnetic insulator and an heterostructure of TBG adjacent to a monolayer of a transition metal dichalcogenide. We show that the Gilbert damping of the ferromagnetic resonance experiment through this junction depends on the twist angle of TBG, and shows a sharp drop at the MA. Our results open the way to a twist switchable spintronics in twisted van der Waals heterostructures.

Several numerical studies have shown that the electronic properties of twisted bilayers of graphene (TBLG) and transition metal dichalcogenides (TMDs) are tunable by strain engineering of the stacking layers. In particular, the flatness of the low-energy moiré bands of the rigid and the relaxed TBLG was found to be, substantially, sensitive to the strain. However, to the best of our knowledge, there are no full analytical calculations of the effect of strain on such bands. We derive, based on the continuum model of moiré flat bands, the low-energy Hamiltonian of twisted homobilayers of graphene and TMDs under strain at small twist angles. We obtain the analytical expressions of the strain-renormalized Dirac velocities and explain the role of strain in the emergence of the flat bands. We discuss how strain could correct the twist angles and bring them closer to the magic angle of TBLG and how it may reduce the widths of the lowest-energy bands at charge neutrality of the twisted homobilayer of TMDs. The analytical results are compared with numerical and experimental findings and also with our numerical calculations based on the continuum model.

Understanding the microscopic origins of the competition between spin and charge degrees of freedom is a central challenge at the heart of strongly correlated many-body physics. Recently, the combination of optical tweezer arrays with systems exhibiting strong interactions, such as Rydberg atoms or ultracold polar molecules, has opened the door for quantum simulation platforms to explore a wide variety of spin models. A significant next step will be the combination of such settings with mobile dopants, in order to study the physics of doped quantum magnets. Here we present recent numerical results from large-scale density matrix renormalization group (DMRG) calculations investigating the phase diagram of the bosonic t-J model with cylindrical boundary conditions at low doping. By introducing antiferromagnetic (AFM) couplings between neighbouring spins, we realize competition between the charge motion and magnetic order similar to that observed in high-Tc cuprates. In the case of only two holes–the simplest instance in which the underlying bosonic statistics plays a role–our results indicate a strong tendency for bosonic holes to form stripes, as observed by the emergence of a domain wall in the local spin-spin correlation function. In contrast, identical simulations performed for the standard fermionic t-J model show that fermionic holes prefer to form tightly bound pairs. We also present our recent experimental proposal to realize 2D AFM bosonic t-J models in optical tweezer arrays via encoding the local Hilbert space in a set of three internal atomic or molecular states.

The natural mineral atacamite $Cu_2Cl(OH)_3$ was found to feature the coupling scheme of a non-uniform quantum sawtooth chain with $J = 336$ K along the basal sites of the chain and $J’ = 102$ K within the sawteeth [1]. The magnetization of this frustrated material is plateau-like with $M \sim M_\mathrm{sat}/2$ in high magnetic fields, but which was found to be unrelated to the $1/2$-plateau of the sawtooth chain [1]. Here, we present high-field heat capacity data of atacamite for $\mathbf{H} \parallel c$ axis, where the plateau-like magnetization sets in at 21.9 T. We found evidence for a field-induced quantum critical point in atacamite, which seems to separate the field region of the antiferromagnetic phase present in lower magnetic fields and a field region without long-range magnetic order in higher magnetic fields. [1] L. Heinze, H. O. Jeschke, I. I. Mazin, A. Metavitsiadis, M. Reehuis, R. Feyerherm, J.-U. Hoffmann, M. Bartkowiak, O. Prokhnenko, A. U. B. Wolter, X. Ding, V. S. Zapf, C. Corvalán Moya, F. Weickert, M. Jaime, K. C. Rule, D. Menzel, R. Valentí, W. Brenig, and S. Süllow, Phys. Rev. Lett. 126, 207201 (2021).

The spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice exhibits a rich ground-state phase diagram in a magnetic field [1]. We investigate the thermodynamic properties of this model using a combination of analytical and numerical methods, including full diagonalization up to effectively $N=30$ sites. We focus in particular on the vicinity of a “dimer-tetramer” phase at low magnetic fields that maps to a classical dimer model on the square lattice and retains a macroscopic ground-state degeneracy in a magnetic field. We discuss the consequences of this degeneracy for the thermodynamic and magnetocaloric properties of the system. [1] N. Caci, K. Karl'ová, T. Verkholyak, J. Strečka, S. Wessel, A. Honecker, Phases of the Spin-1/2 Heisenberg Antiferromagnet on the Diamond-Decorated Square Lattice in a Magnetic Field, Phys. Rev. B 107 (2023) 115143

The low-lying excitations of metals are remarkably well explained by effective single-particle theories of non-interacting bands in which correlations are described by a renormalization of the band properties. Yet, strong interactions are abundant in essentially all materials. This raises the question for direct spectroscopic signatures of phenomena beyond effective single-particle, single-band behaviour. Here, we report on such a signature in the quantum oscillations (QOs) of the three-dimensional topological semimetal CoSi [1]. The remarkably simple, well understood QO spectrum of CoSi related to Fermi surface pockets around the R-point [2-4] allowed us to identify a QO frequency which defies the standard description in two fundamental aspects. First, the oscillation frequency corresponds to the difference of semi-classical quasi-particle (QP) orbits of two bands although the composite orbit is forbidden as half of the trajectory would oppose the Lorentz force. Second, the oscillations exist up to above 50 K - in stark contrast to all other oscillatory components - which already vanish below a few K. We show that our findings are in excellent agreement with QOs of the QP lifetime. Since the only precondition for this effect is a non-linear coupling of at least two quasiparticle orbits under magnetic field, e.g., due to QP scattering on defects or collective excitations, such QOs of the QP lifetime are generic for any metal featuring Landau quantization. Representing QO frequencies without corresponding Fermi surface cross-sections, QOs of the QP lifetime offer an unexpected new perspective on key observations reported in materials such as the FeAs- and cuprate-superconductors, multifold- and heavy-fermion compounds, as well as Rashba-systems. Moreover, QOs of the QP lifetime promise to provide a powerful tool for the identification of new correlation phenomena in two-dimensional materials as well as bulk multiband metals. References: [1] N. Huber et al., Nature, in production (2023) [2] N. Huber et al., Phys. Rev. Lett. 129, 026401 (2022) [3] C. Guo et al., Nat. Phys. 18, 813 (2022) [4] M. A. Wilde et al., Nature 594, 374-379 (2021)

Laughlin states have recently been constructed on fractal lattices, and the charge and braiding statistics of the quasiholes were used to confirm that these states have Laughlin type topology. Here, we investigate density, correlation, and entanglement properties of the states on a fractal lattice derived from a Sierpinski triangle with the purpose of identifying similarities and differences compared to two-dimensional systems and with the purpose of investigating whether various probes of topology work for fractal lattices. Similarly to two-dimensional systems, we find that the connected particle-particle correlation function decays roughly exponentially with the distance between the lattice sites measured in the two-dimensional plane, but the values also depend on the local environment. Contrary to two-dimensional systems, we find that the entanglement entropy does not follow the area law if one defines the area to be the number of nearest neighbor bonds that cross the edge of the selected subsystem. Considering bipartitions with two bonds crossing the edge, we find a close to logarithmic scaling of the entanglement entropy with the number of sites in the subsystem. This also means that the topological entanglement entropy cannot be extracted using the Kitaev-Preskill or the Levin-Wen methods. Studying the entanglement spectrum for different bipartitions, we find that the number of states below the entanglement gap is robust and the same as for Laughlin states on two-dimensional lattices.

Topological properties of quantum systems are one of the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have demonstrated topological phases of matter in various quantum systems. However, using the robustness of such modes to stabilize quantum correlations is still a highly sought-after milestone. In this work, we put forward a concept of using topological modes to stabilize fully entangled quantum states, and we demonstrate the stability of the entanglement with respect to parameter fluctuations. Specifically, we see that entanglement remains stable against parameter fluctuations in the topologically non-trivial regime, while entanglement in the trivial regime is highly susceptible to local noise. We supplement our scheme with an experimentally realistic and detailed proposal based on coupled superconducting resonators and qubits. Our proposal sets a novel approach for generating long-lived quantum modes with robustness towards disorder in the circuit parameters via a bottom-up experimental approach relying on easy-to-engineer building blocks.

The behavior of a spin liquid upon the introduction of a single hole is a pertinent open question. This is of experimental relevance, as the hole spectral function, measured momentum-resolved in angle-resolved photoemission spectroscopy or locally in scanning tunneling microscopy, can be used to identify spin liquid materials. In this study, we employ tensor network methods to simulate the time evolution of a single hole doped into the Kitaev spin-liquid ground state. Our investigations reveal two fundamentally different scenarios for the fate of spin liquids upon single-hole doping. For the Kitaev model, the response critically depends on the sign of the spin couplings. For ferromagnetic couplings, the spin liquid gets destroyed by a single hole, even at weak coupling. Instead, a Nagaoka ferromagnet forms dynamically. Conversely, in the case of antiferromagnetic couplings, the hole spectrum demonstrates an intricate interplay between charge, spin, and flux degrees of freedom, best described by a parton mean-field ansatz of fractionalized holons and spinons. Moreover, we find a good agreement of our numerical results to the previously studied case of slow holes, which is exactly solvable.

The mixed-spin Heisenberg octahedral chain in a magnetic field has an extraordinarily rich ground-state phase diagram including the uniform and cluster-based Haldane phases, two ferrimagnetic phases of Lieb-Mattis type, quantum spin liquids, bound-magnon crystal in addition to the fully polarized ferromagnetic phase. It is shown that the lowest-energy eigenstates of the mixed-spin Heisenberg octahedral chain belong to flat bands, which allow a precise description of low-temperature magnetic properties within the localized-magnon approach exploiting >> a classical lattice-gas model of hard-core monomers and dimers in moderately and highly frustrated parameter regions. A comparison between results of the >> developed localized-magnon theory and accurate numerical methods like full exact diagonalization and finite-temperature Lanczos methods will be provided.

Kagome metals have been extensively studied for their anomalous transports observed in the low-temperature and room-temperature ordered phases. Here, we show that even the elevated temperature disordered phase of a kagome metal exhibits an unconventional spin transport due to emergent constraints, which manifests as a measurable spectral distribution in a dynamic spin structure factor. We consider the strong-coupling limit of an extended Hubbard model on the kagome lattice with 2/3 filling, where the interplay between strong electron correlations and geometrical frustration leads to total spin conservation laws on dynamically moving sublattices, serving as exotic constraints. Employing a cellular automaton circuit with the constraints, we numerically demonstrate how the constraints drastically alter the late-time spin transport. We also discuss an unconventional charge transport that emerges from the constraints, which can be explained by the Gaussian field theory of a scalar height field.

In extended Heisenberg-Kitaev-Gamma-type spin models, hidden-SU(2)-symmetric points are isolated points in parameter space that can be mapped to pure Heisenberg models via nontrivial duality transformations. Such points generically feature quantum degeneracy between conventional single-Q and exotic multi-Q states. We argue that recent single-crystal inelastic neutron scattering data place the honeycomb magnet Na$_2$Co$_2$TeO$_6$ in proximity to such a hidden-SU(2)-symmetric point. The low-temperature order is identified as a triple-Q state arising from the Neel antiferromagnet with staggered magnetization in the out-of-plane direction via a 4-sublattice duality transformation. This state naturally explains various distinctive features of the magnetic excitation spectrum, including its surprisingly high symmetry and the dispersive low-energy and flat high-energy bands. Our result demonstrates the importance of bond-dependent exchange interactions in cobaltates, and illustrates the intriguing magnetic behavior resulting from them.

Motivated by recent discovery of the non-magnetic Ising transition, at which the energy gap of magnetic excitations remains open, we search for other types of non-magnetic phase transitions that can be realized in quantum spin chains. In this work we focus on a new chiral transition recently reported in the context Rydberg atoms between the period-four and disorder phase. To explore whether chiral transitions can also be realized in quantum spin chains, we look at the quantum loop model, i.e. an effective model of spin-1 ladder with a constrained Hilbert space limited to the singlet sector only. We use extensive density-matrix renormalization group simulations to show the presence of chiral perturbations and to unveil how this affect the nature of the quantum phase transitions between the plaquette (period-four) and the next-nearest-neighbor Haldane (disordered) phases.

Fractons are a class of particles that exhibit constrained mobility, most commonly associated with the presence of unusual conservation laws. Recent works investigating the hydrodynamics of fractonic fluids have revealed that their flow is possible only when these conservation laws are spontaneously broken, rendering them superfluids. In this presentation I will discuss this scenario on a specific example (system with dipole and quadrupole conservation laws) and show how adding a dynamical gauge field into the picture leads to the appearance of fractonic superconductors.

We formulate a Landau theory for altermagnets, a class of colinear compensated magnets with spin-split bands. Starting from the non-relativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space symmetries, providing a simple framework for understanding the key features of this family of materials. We find a set of multipolar secondary order parameters connecting existing ideas about the spin symmetries of these systems, their order parameters and the effect of non-zero spin-orbit coupling. We account for several features of canonical altermagnets such as RuO2, MnTe and CuF2 that go beyond symmetry alone, relating the order parameter to key observables such as magnetization, anomalous Hall conductivity and magneto-elastic and magneto-optical probes.

We identify an exotic quasiuniversal behavior near the all-in-all-out Weyl quantum critical point in three-dimensional Luttinger semimetals, such as the pyrochlore iridates $R_2$Ir$_2$O$_7$, with $R$ a rare-earth element. The quasiuniversal behavior is characterized by power laws with exponents that vary slowly over several orders of magnitude in energy or length. However, in contrast to the quasiuniversality discussed in the context of deconfined criticality, the present case is characterized by a genuinely-universal ultra-low-temperature behavior. In this limit, the pertinent critical exponents can be computed exactly within a renormalization group analysis. Experimental implications for the pyrochlore iridates are outlined.

Measurement-based quantum computing (MBQC), an alternate paradigm for formulating quan- tum algorithms, can lead to potentially more flexible and efficient implementations as well as to theoretical insights on the role of entanglement in a quantum algorithm. Using the recently developed ZX-calculus, we outline a general scheme for reformulating quantum circuits as MBQC implementations. After illustrating the method using the two-qubit Deutsch-Jozsa algorithm, we derive a ZX graph-diagram that encodes a general MBQC implementation for the three-qubit Deutsch-Jozsa algorithm. This graph describes an 11-qubit cluster state on which single-qubit measurements are used to execute the algorithm. Particular sets of choices of the axes for the measurements can be used to implement any realization of the oracle. In addition, we derive an equivalent lattice cluster state for the algorithm.

In this work we build on a previous study on topology in the interacting Hubbard diamond chain.[1] Previously, this has been understood using the topological Hamiltonian, calculated from the Green’s function obtained via the cluster perturbation theory (CPT) method. Here we extend the analysis by including spin-orbit coupling and investigating the effect that different magnitudes of spin-orbit coupling have on the phase diagram. Of particular interest is how spin-orbit coupling changes the Mott insulating phase previously found. As Mott phases are difficult to be described by formalisms such as Topological Quantum Chemistry (TQC) and even the topological Hamiltonian approach fails to capture their features, we are employing other Green’s function based methods (boundary and bulk zeros of the Green’s function,[2] Berry curvature and phases computed from Green’s function eigenvectors[3]) and testing their applicability to our model. [1] M. Iraola et al., Phys. Rev. B 104, 195125 (2021) [2] N. Wagner et al., https://arxiv.org/abs/2301.05588 (2023) [3] C. Setty et al., https://arxiv.org/abs/2301.13870 (2023)

Revealing the existence of hidden off-diagonal long range order is believed to be a promising avenue towards identifying and characterizing topological order. In continuum fractional quantum Hall systems this can be accomplished by attaching gauge flux tubes onto the particles. Following the recent advances of cold atom experiments in optical lattices, probing this hidden, non-local order parameter with Fock-basis snapshots for lattice analogs is now within reach. Here, we demonstrate the existence of hidden off-diagonal long range order in quasi two-dimensional lattices in the $\nu=1/2$-ground state of the experimentally realistic isotropic Hofstadter-Bose-Hubbard model. To this end, we provide a MPS-driven, hybrid one and two-site snapshot procedure to sample the one-particle reduced density matrix and all particle positions simultaneously, emulating an experimentally feasible protocol. We present strong numerical indications for the emergence of an algebraic decay and discuss the resolution achievable using only few snapshots.

We present the analysis of the slowing down exhibited by stochastic dynamics of a ring-exchange model on a square lattice, by means of numerical simulations. We find the preservation of coarse-grained memory of initial state of density-wave types for unexpectedly long times. This behavior is inconsistent with the prediction from a low frequency continuum theory developed by assuming a mean-field solution. Through a detailed analysis of correlation functions of the dynamically active regions, we exhibit an unconventional transient long ranged structure formation in a direction which is featureless for the initial condition, and argue that its slow melting plays a crucial role in the slowing-down mechanism. We expect our results to be relevant also for the dynamics of quantum ring-exchange dynamics of hard-core bosons and more generally for dipole moment conserving models.

Frustrated magnets are a result of competing interactions. These systems are of interest because they can exhibit a large ground state degeneracy, sometimes in the form of an emergent symmetry. We study the effect of off-diagonal symmetric exchange interactions on classical Heisenberg spins on the Kagome and Hyperkagome lattices. We find an emergent U(1) symmetry in the ground state. We study the critical properties and the influence of thermal order-by-disorder on this symmetry using a combination of analytical and Monte Carlo methods. This emergent symmetry can be understood on the level of a single triangle. Using this understanding, we propose a set of rules to generate a lattice model with these off-diagonal interactions that will exhibit the same emergent U(1) symmetry.

Highly frustrated quantum spin systems are in the focus of theoretical and experimental studies due their unconventional properties such as highly entangled spin-liquid ground states and fractionalized excitations. The most prominent example is the s=1/2 kagome Heisenberg antiferromagnet (HAFM). Very recently the square-kagome HAFM has come into the focus as another promising candidate of a quantum spin-liquid material. So far the theoretical studies of the s=1/2 kagome as well as square-kagome HAFM are focussed on ground state properties, whereas much less is known on thermodynamics. We fill this gap by large scale numerical simulations of both models using the finite-temperature Lanczos method for system sizes of $N=18,24,30,36,42,48$, and $54$. We find a striking similarity of the temperature profiles of the basic thermodynamic properties of the square-kagome and the kagome HAFM down to very low temperatures $T$. The specific heat exhibits a low-temperature shoulder below the major maximum which can be attributed to low-lying singlet excitations filling the singlet-triplet gap, which is significantly larger than the singlet-singlet gap. This observation is further supported by the behavior of the entropy $S(T)$, where a change in curvature is present just at about $T/J=0.2$, the same temperature where the shoulder in $C$ sets in. For the susceptibility the low-lying singlet excitations are irrelevant, and the singlet-triplet gap leads to an exponentially activated low-temperature behavior. The maximum in $\chi(T)$ is found at a pretty low temperature $T_{\rm max}/J=0.146$ compared to $T_{\rm max}/J=0.935$ for the unfrustrated square-lattice HAFM signaling the crucial role of frustration also for the susceptibility. The magnetization process featuring plateaus and jumps and the field dependence of the specific heat that exhibits characteristic peculiarities attributed to the existence of a flat one-magnon band are as well discussed.

Magnetic skyrmions are vortex-like quasiparticles characterized by long lifetime and remarkable topological properties. These properties make them a promising candidate for the role of information carriers in magnetic information storage and processing devices. Although considerable progress has been made in studying skyrmions in classical systems, little is known about skyrmions in quantum systems: they cannot be directly observed by probing the local magnetization of the system, and the notion of topological protection is elusive in the quantum realm. Here, we explore the potential robustness of quantum skyrmions in comparison to their classical counterparts. We theoretically analyze the dynamics of a quantum skyrmion subject to local projective measurements and demonstrate that the quantum scalar chirality, that characterize the quantum skyrmion, changes very little upon external perturbations. We further show that by performing repetitive measurements on a quantum skyrmion, it can be completely stabilized through an analogue of the quantum Zeno effect.

Non-Hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a non-diagonalizable Jordan block. It is known that symmetries can enhance the abundance of exceptional points in noninteracting systems. Here we investigate the fate of such symmetry-protected exceptional points in the presence of a symmetry-preserving interaction between fermions and find that (i) exceptional points are stable in the presence of the interaction. Their propagation through the parameter space leads to the formation of characteristic exceptional “fans.” In addition, (ii) we identify a new source for exceptional points that are only present due to the interaction. These points emerge from diagonalizable degeneracies in the noninteracting case. Beyond their creation and stability, (iii) we also find that exceptional points can annihilate each other if they meet in parameter space with compatible many-body states forming a third-order exceptional point at the endpoint. These phenomena are well captured by an “exceptional perturbation theory” starting from a noninteracting Hamiltonian. [1] Robin Schäfer, Jan C. Budich, and David J. Luitz, Phys. Rev. Research 4, 033181

The kagome lattice Heisenberg antiferromagnet (KHAF) is a rich source of unconventional physics not only regarding its spin-liquid ground state but also with respect to its behavior at non-zero field and temperature. Here we investigate the magnetization as well as the specific heat in a wide range of temperature and field in view of two aspects. The first concerns the asymmetric melting of the magnetization plateau at 1/3 of the saturation magnetization, see figure and Refs.K42,MMY. We explain the effect by discussing the energy diagram and the density of states constructed from finite-temperature Lanczos data for KHAF with up to 48 sites (CHE). The second aspect concerns the specific heat as function of $T$ and $B$ where we discuss the relation of local maxima to possible phase transitions in the thermodynamic limit, such as magnon crystallization (MC). K42: J. Schnack, J. Schulenburg, J. Richter, Phys. Rev. B 98, 094423 (2018) MMY: Takahiro Misawa, Yuichi Motoyama, and Youhei Yamaji, Phys. Rev. B 102, 094419 (2020) CHE: H. Schlüter, F. Gayk, H.-J. Schmidt, A. Honecker, J. Schnack, Z. Naturforsch. A 76, 823-834 (2021) MC: J. Schnack, J. Schulenburg, A. Honecker, J. Richter, Phys. Rev. Lett. 125, 117207 (2020)

We use real-space Hartree-Fock theory to construct a magnetic phase diagram of the 2D Hubbard model as a function of temperature and doping. We are able to detect various spin- and charge order patterns including Néel, stripe and spiral order without biasing the system towards one of them. For an intermediate interaction strength, we predominatly find Néel order close to half-filling, stripe order for low temperatures or large doping and an intermediate region of spiral order.

Superconductivity has, since 1911, become a pillar and a flagship of condensed matter physics. The main paradigm is given by BCS theory which, in its standard form, consists of quasiparticles in a single, partially filled band, pairing and thus condensating in a collective dissipationless state. This single band approximation has its limits. Indeed, since the 1980s, physicists have come to realize that in a multiband setting, even adiabatic, each band will carry an influence of the other bands in the form of two geometric quantities, namely the Berry curvature and the quantum metric. These quantities form what we call band/quantum geometry. In the context of superconductivity, this means that even if a single band is involved in the Cooper pairing, it can carry a quantum geometry if the normal state has more than one band. The influence of this normal state's quantum geometry on the superconducting state is the subject of this talk. On one side, we study the influence of the normal state’s Berry curvature on BCS theory in the context of two-dimensional massive Dirac fermions. We find that it generally lowers the critical temperature, in a quantifiable way. On another side, we consider the (111) $\text{LaAlO}_3/\text{SrTiO}_3$ interface. Our results there suggest a sizeable influence of the normal state's quantum metric in the overdoped regime of the observed superconducting dome, as well as the formation of a second superconducting dome, purely coming from the normal state's quantum metric.

Modern scanning probe techniques, like scanning tunneling microscopy (STM), provide access to a large amount of data encoding the underlying physics of quantum matter. In this work, we analyze how convolutional neural networks (CNN) can be employed to learn effective theoretical models from STM data on correlated moir\'e superlattices. These engineered systems are particularly well suited for this task as their enhanced lattice constant provides unprecedented access to intra-unit-cell physics and their tunability allows for high-dimensional data sets within a single sample. Using electronic nematic order in twisted double-bilayer graphene (TDBG) as an example, we show that including correlations between the local density of states (LDOS) at different energies allows CNNs not only to learn the microscopic nematic order parameter, but also to distinguish it from heterostrain. These results demonstrate that neural networks constitute a powerful methodology for investigating the microscopic details of correlated phenomena in moir\'e systems and beyond.

Rydberg atoms have become an ideal platform for studying isolated quantum many-body systems. By controlling the laser detuning and the inter-atomic distance, one can investigate diverse critical phenomena, in particular, the commensurate-incommensurate quantum phase transitions. Our approach involves numerical simulation of critical real-time dynamics within non-equilibrium chains of Rydberg atoms. Utilizing the time-evolving block decimation algorithm, we decode the intricacies of the commensurate-incommensurate phase transition via the application of the Kibble-Zurek mechanism and Finite-Time Scaling. We study the isolated conformal points surrounded by the new chiral quantum phase transition types with an effective blockade model where a constraint of no double occupancy replaces the short-distance repulsions. Combining the Kibble-Zurek mechanism with the Finite-Time Scaling theory, we extract all major critical exponents – $\nu$, $z$ and $\beta$. The implications of the finite-size effect will be briefly discussed.

The nature of states in the quantum Hall regime of graphene in higher Landau levels remains poorly understood partly because of the lack of a model that captures its valley-dependent symmetry breaking interactions. In this paper we develop systematically such a model, which interestingly, and in contrast to the N=0 Landau level, features not only pure δ function interactions, but also some of its derivatives. We show that this model can lead to qualitatively new ground states relative to the N=0 Landau level, such as ground states with entangled spin and valley degrees of freedom that compete with simpler broken symmetry states. Moreover, at half-filling we have found a new phase that is absent in the N=0 Landau level which combines characteristics of a valence-bond solid and an antiferromagnet. We discuss the estimation of parameters of this model based on recent compressibility experiments.

While the Haldane model for the anomalous Hall effect is usually inspected in relation to one-dimensional topological states, manipulating the edge modes can also lead to the emergence of fractionally charged zero dimensional Jackiw-Rebbi like excitations. I will here address two models in which such excitations are due to the coupling between pairs of edge modes. The first is a quasicrystalline second order topological insulator, consisting of two coupled layers of Haldane model with a relative 30 degree twist and opposite Chern numbers. The second is a thin strip of Haldane model, in which the coupling between the chiral edge modes is due to spatial proximity and give rise to multiple topological phase transitions. I will show that the effective mass term of the low energy theory describing the bound states and, consequently, the value of the associated fractional charge, crucially depends on the model considered and, given the model, on the nature of the edges which are coupled together. More generally, I hence demonstrate that the simple low energy representation of the chiral edges is largely insufficient to describe experimentally relevant topological nanostructures.

Quantum spin liquids are tantalizing phases of frustrated quantum magnets. A complicating factor in their realization and observation in materials is the ubiquitous presence of other degrees of freedom, in particular lattice distortion modes (phonons), that provide additional mechanisms for relieving magnetic frustration, thereby possibly spoiling spin-liquid ground states. In this work, we focus on triangular-lattice Heisenberg antiferromagnetic, where recent numerical evidence suggests the presence of an extended U(1) Dirac spin liquid phase which is described by compact quantum electrodynamics in 2+1 dimensions (QED$_3$), featuring gapless spinons and monopoles as gauge excitations. The theory is believed to flow to a strongly-coupled fixed point with conformal symmetries at low energies. Using complementary perturbation theory and scaling arguments, we show that a symmetry-allowed coupling between finite-wavevector lattice distortions and monopole operators of the U(1) DSL induces a spin-Peierls instability towards a (confining) 12-site valence-bond solid state. We support our theoretical analysis by state-of-the-art iDMRG simulations. Away from the limit of static distortions, we demonstrate that the phonon energy gap establishes a parameter regime where the spin liquid is expected to be stable.

Lorentz symmetry is commonly assumed to be an intrinsic requirement of the (2+1)d deconfined quantum phase transition (DQPT), and the conformal field theory (CFT) can be utilized. The dynamics of DQPT in the Kagome lattice are explored by using a combination of large-scale quantum Monte Carlo simulations and stochastic analytic continuation. In the valence-bonded solid phase, the fragmentation of a nearly flat band with a finite energy gap is observed around the K point. At the deconfined quantum critical point, besides the linear dispersion at the $\Gamma$ point, another one is found at the K point. Counterintuitively, these two gapless modes take different speeds equal to 0.319(8) and 0.101(9), indicating the absence of Lorentz symmetry. After carefully inspecting the snapshot of the simulation, we discovered the fast mode at the $\Gamma$ point corresponds to the deconfinement of spinons (fractional charges), and the slow mode at the K point is related to the quantum string (generalized symmetry). Our work will extend the understanding of phase transition, and intrigue the field of topological quantum field theory.

We investigate the antiferromagnetic transverse field Ising model on the triangular lattice through large-scale quantum Monte Carlo simulations and stochastic analytic continuation. This model effectively describes a series of triangular rare-earth compounds but also the numerous quantum simulation platforms, e.g. Rydberg arrays. At the weak transverse field, we capture the excitations related to topological quantum strings, which exhibit continuum features described by XY chain along the strings and those in accord with ‘Luttinger string liquid’ in the perpendicular direction. The continuum features can be well understood from the perspective of topological strings. Furthermore, we identify the contribution of strings from the excitation spectrum. Our study provides characteristic features for the experimental search for string-related excitations and proposes a theoretical method to pinpoint topological excitations in the experimental spectra.