Korrelationstage 2017

In recent years, because of the emergence of candidate materials and the interest in the spin liquid state realization, there has been a growing number of studies on the Kitaev model, at first, and on the Kitaev-Heisenberg (KH) after. Adding the Heisenberg type interaction to the initial, exactly integrable, model is necessary and inevitable for any realistic description, but leads to spin frustration. Nevertheless, the vast majority of these studies is focused on 2-dimensional lattices (honeycomb, triangular), while research on the KH chain is lacking. Motivated by this, we study the KH chain using the exact diagonalization and the density matrix renormalization group techniques. We present the phase diagram as a function of an angle parameter $\phi$, setting the Heisenberg interaction to $\cos\phi$ and the Kitaev one to $\sin\phi$. By calculating total spin, spin-spin correlations, correlation length, central charge, static structure factor, and order parameters, we identify six different possible phases; namely, Tomonaga-Luttinger liquid, spiral-XY, Sz-ferromagnetic, ferromagnetic, staggered-XY and N\'eel phases. Two Kitaev points $\phi=\frac{\pi}{2}$ and $\phi=\frac{3\pi}{2}$ are singular. The $\phi$-dependent phase diagram is similar to that for the honeycomb-lattice KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We also discuss the magnetic structure of the K-intercalated RuCl$_3$, celebrated as a potential Kitaev material, in the framework of the 1D KH model.

Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics, respectively. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure initial state maintains the system globally at zero entropy, at long time after the quench local properties are captured by an appropriate statistical ensemble with non zero thermodynamic entropy, which can be interpreted as the entanglement accumulated during the dynamics. Therefore, understanding the post-quench entanglement evolution unveils how thermodynamics emerges in isolated quantum systems. An exact computation of the entanglement dynamics has been provided only for non-interacting systems, and it was believed to be unfeasible for genuinely interacting models. Conversely, here we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the asymptotic state, leads to a complete analytical understanding of the entanglement dynamics in the space-time scaling limit. Our framework requires only knowledge about the steady state, and the velocities of the low-lying excitations around it. We provide a thorough check of our result focusing on the spin-1/2 Heisenberg XXZ chain, and considering quenches from several initial states. We compare our results with numerical simulations using both tDMRG and iTEBD, finding always perfect agreement. References: Vincenzo Alba and Pasquale Calabrese, PNAS, 10.1073/pnas.1703516114

Topological Kondo insulators (TKI) have recently been proposed as a new system where a gap at the Fermi energy and, subsequently, a non-trivial topological phase are created by strong correlations [1]. The present work investigates the influence of the finite life-time of the heavy Kondo quasiparticles on the stability of a TKI phase. Because of the strong spin-orbit (SO) coupling within the rare-earth 4f-orbitals of a heavy-fermion system, the local ground-state Kramers doublet involves mixing of spin and orbital degrees of freedom. This leads to a topological term in the hybridization of the 4f- and the conduction band [1]. Using slave-boson mean field theory [2], we calculate the band structure of a 3D bulk TKI. We then calculate the layer-dependent band structure near a 2D surface of a 3D TKI. Finite quasiparticle life-time effects are incorporated by taking bosonic fluctuations about the mean field solution into account and by calculating the corresponding self-energies. We aim at calculating characteristic, observable quantities, like the surface conductivity, including life-time effects. [1] M. Dzero, et al., Ann. Rev. Cond. Matt. 7, 249-280 (2016). [2] V. Alexandrov, et al., Phys. Rev. Lett. 114, 177202 (2015).

We employ the pseudo-fermion functional renormalization group (PFFRG) method to study the ground state properties of quantum Heisenberg models in two and three dimensions with variable spin length S. We first present a brief introduction to the PFFRG method and show how it can be used to simulate magnetic properties of 2D and 3D quantum magnetic materials. Particularly, by adding an extra spin degree of freedom to the pseudo fermions we are able to compute the magnetic susceptibility for arbitrary values of S, including the classical limit $S\rightarrow\infty$. We confirm that even without explicitly projecting onto the highest spin sector of the Hilbert space, ground states tend to select the largest possible local spin magnitude. This justifies the average treatment of the pseudo fermion-constraint in previous spin-1/2 PFFRG studies. We present results for three different systems: First, to show the validity of the approach for 3D systems and to demonstrate the calculation of critical ordering temperatures, we present the phase diagram for the ferromagnetic and antiferromagnetic Heisenberg model on the BCC lattice, with first ($J_1$), second ($J_2$), and third neighbor interactions ($J_3$), for a spin length $S=1/2$. We find that for ferromagnetic and antiferromagnetic $J_1$, frustration effects generate a large non-magnetic intermediate phase. As a benchmark for the extension to arbitrary S, we further study a honeycomb Heisenberg model with first and second neighbor couplings and spins ranging from $S=1/2$ to $S=3$. Mapping out the phase diagram in the $J_2/J_1$-$S$ plane we find that upon increasing $S$ quantum fluctuations are rapidly decreasing. In particular, already at $S = 1$ we find no indication of a magnetically disordered phase. Furthermore, we show that in the classical limit the PFFRG equations can be solved analytically and the method becomes identical to the Luttinger-Tisza method. Finally, we combine both approaches and display the results for the pyrochlore Heisenberg model with variable spin length. We present the phase diagrams as a function of $J2/J1$ for spin lengths $S=1/2$, $S=1$, and $S=3/2$, and show that a non-magnetic phase survives up to $S=1$.

I will present the newly developed Fork Tensor Product States (FTPS) multiorbital impurity solver. Since our approach works on the real frequency axis no ill-posed analytic continuation is needed. Good resolution at all energies allows us to resolve and analyze multiplet-structure in Hubbard bands. Starting at the prototypical benchmark material $SrVO_3$, new results for the Mott-insulator $SrMnO_3$ even for full five-band calculations by including the $e_g$ states to the $t_{2g}$ orbitals.

We propose a measurement scheme to experimentally access the momentum and energy resolved spectral function in a quantum gas microscope with currently available techniques. We furthermore present numerical results for the excitation spectrum of a single hole in an antiferromagnetic spin chain. In finite systems, spin-charge separation can be observed across the entire spectrum and a full resolution of the spinon dispersion is possible. Remarkably, a sharp asymmetry in the distribution of spectral weight, reminiscent of pseudogap phenomenology in two-dimensional cuprates, appears for the isotropic Heisenberg spin chain. We discuss a slave-fermion mean field theory for quantum spin liquids that captures the essential features of the observed behavior.

We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest neighbor and three-site interactions using extensive numerical simulations and a conformal field theory analysis. We show that the transition can be second order in the WZW SU(2)$_2$ or Ising universality class, or first-order. We provide an explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. We explain how to use the DMRG/MPS algorithm to calculate efficiently the excitation spectra of one-dimensional critical systems. The described method has been benchmarked on the critical transverse-field Ising model. We suggest that the choice between WZW SU(2)_2 and Ising universality class depends on the nature of the domain walls between the corresponding phases. The results have been generalized to larger spins. In particular, we explain how the conformal field theory combined with computed excitation spectra can be used to locate Kosterlitz-Thouless phase transition in half-odd integer spin chains.

The experimental realization of the Harper-Hofstadter model in ultra-cold atomic gases has placed fractional states of matter in these systems within reach; by half-filling the lowest band a fractional Chern insulator state (FCI) is expected to emerge. These experiments naturally probe the dynamics of this topological state, yet little is known about such properties or how they may differ compared to their non-interacting counterparts. In this Letter we explore, using infinite density matrix renormalization group (iDMRG) simulations, the response of the FCI state in the Harper-Hofstadter model to spatially localized perturbations. After confirming the static properties with superior precision we show that, unlike the free counterpart i) a generic edge perturbation in this model propagates chirally and ii) the chiral dynamics is insensitive to the strength of a local perturbation applied at the edge. Additionally, our simulations show that there is inevitable density leakage into the bulk, preventing a naive chiral Luttinger theory interpretation of the dynamics. Taken as a whole, our results show that the FCI state in the Harper-Hofstadter model can be distinguished from its non-interacting counterpart by measuring the density evolution as a function of time, an observable readily accessible in current experimental set-ups.

Using exact diagonalization analytical results for small clusters (dimers, trimers, squares and tetramers) we derive approximate effective generalized Heisenberg type spin-Hamiltonians valid for any correlation ratio $u= U/t$, where U denotes the on-site Coulomb repulsion and t is the nearest neighbor (NN)-transfer integral. Thereby we present analytical results for the first, second (NNN), and third neighbor exchange integrals $J_1 \gg J_2 \gg J_3$, respectively, and also for the leading cyclic quartic (four spin) exchange terms. All two-spin interaction parameters are smooth monotonous functions of $u$ without any artificial divergence at $u$ = 4 or even at $u$ = 0 as in other methods based on standard weak or strong coupling perturbation theory. Our results compare well with those for the NN (analytical expression) and the NNN (numerical data are available in the limit $u \geq 4$, only) exchange integrals $J_1$ and $J_2$, respectively, obtained within the flow-equation technique \cite{Hamerla2010}. In the strong coupling limit NN and NNN exchange interaction dominate the effective spin Hamiltonian whereas in the weak coupling limit cyclic exchange couplings become comparable with or are even larger than the antiferromagnetic NN and NNN exchange terms $J_1$ and $J_2$. Possible applications to $\pi$-electron carbon based "conducting" polymers such as polyacetylene and polyyne and other spin-Peierls systems being in the intermediate coupling regime are shortly mentioned. We briefly consider also generalizations of the simple 1D Hubbard model including NNN hoppings $t_2$, the intersite Coulomb interaction $V$ as well as an arbitrary direct exchange term J as an effective model for strongly frustrated edge-sharing cuprate chain compounds usually described in five-band Hubbard Cu 3$d$ O 2$p$ models with dominant ferromagnetic inter-($CuO_4$) plaquette-couplings. [1] S.A. Hamerla {\it et al.}, Phys. Rev. B {\bf 82}, 235117 (2010). S.A. Hamerla and G. Uhrig, unpublished.

We consider an XXZ spin chain in the presence of a magnetic field gradient. The gradient induces an interface between oppositely magnetized regions, with nontrivial profiles of the magnetization and entanglement. We show that the magnetization profile can be captured by combining a local density approximation argument with Bethe Ansatz techniques. The entanglement profile can be recovered using a recently introduced curved-space CFT approach. We also consider the time evolution of the profiles after the gradient is switched off. It is shown that the front profile can be partly recovered using a generalized hydrodynamic approach.

We analyze the static and dynamic properties of the one-dimensional extended anyon-Hubbard model (EAHM) with nearest-neighbor repulsion between the particles, for mean particle density one, exploiting the unbiased matrix-product-state based density-matrix renormalization group (DMRG) technique. We provide compelling evidence for a nontrivial topologial Haldane phase, despite a broken reflection parity symmetry [1]. The Haldane insulator is protected by combined (modified) spatial-inversion and time-reversal symmetries. With regard to an experimental verification of the anyonic Haldane insulator, e.g., in optical lattices setups, the asymmetry of the dynamical density structure factor found should be of particular importance. [1] F. Lange, S. Ejima, and H. Fehske, PRL 118, 120401 (2017).

In previous studies it has been shown, that the non-equilibrium response of superconductors allows for probing of the amplitude-, or Higgs-, mode of the superconducting condensate [1]. This feature was predicted in theory with different quenching protocols [2,3] and found in experiments using ultra-short laser pulses in the THZ Regime [4]. So far only s-wave superconductors with a constant energy gap as a function of momentum have been investigated. For d-wave superconductors the simple interaction quench protocol shows only a single mode as well [5]. In our Poster we present a systematic study of non-equilibrium Higgs oscillations in s- and d-wave superconductors. By using the numerically exact solution of a minimal BCS Model, we show that there exist low energy oscillations which are intrinsic to the superconducting order parameter. No additional degrees of freedom, such as phonons or subleading channels [6], are necessary to induce these modes. We show, however, that the details of the quenching protocol are important in order to address these degrees of freedom. We analyze in detail, how the modes change the superconducting condensate over time to understand its momentum space evolution. Finally, we propose new methods to measure these modes in experiments. [1] E.A. Yuzbashyan, M. Dzero, Phys. Rev. Lett. 96, 230404, (2006) [2] H. Krull, D. Manske, G.S. Uhrig, A.P. Schnyder, Phys. Rev. B 90, 014515 (2014) [3] H. Krull, N. Bittner, G. S. Uhrig, D. Manske, A. P. Schnyder, Nat. Commun. 7, 11921 (2016) [4] R. Matsunaga, R. Shimano Phys. Rev. Lett. 109, 187002, (2012) [5] F. Peronaci, M. Schirò, M. Capone, Phys. Rev. Lett. 115, 257001 (2015) [6] Y. Barlas, C. M. Varma, Phys. Rev. B, 87, 054503 (2013)

We explore the quantum phase transition between symmetry protected topological and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c=7/10. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results.

When a mobile hole is moving in a non-ferromagnetic spin-environment it distorts the surrounding spin correlations, which can lead to the formation of a magnetic polaron. At strong couplings, when the hole hopping rate $t$ is larger than the spin-exchange energy scale $J$, we argue that magnetic polarons can be understood as bound states of a pair of confined partons, a spinon and a holon connected by a geometric string. We predict a series of excited states, invisible in the spectral function, which correspond to rotational excitations of the spinon-holon pair. This is reminiscent of mesonic resonances observed in high-energy physics, which can be understood as rotating quark anti-quark pairs carrying orbital angular momentum. We discuss implications of our theory for the phase diagram of cuprates and show how mesonic bound states can be observed in current experiments with ultracold fermions in quantum gas microscopes.

I present numerical investigation of the quantum distillation process within the Fermi--Hubbard model on a quasi-1D ladder geometry. The term distillation refers to the dynamical, spatial separation of singlons and doublons in the sudden expansion of interacting particles in an optical lattice, i.e., the release of a cloud of atoms from a trapping potential. Remarkably, quantum distillation can lead to a contraction of the doublon cloud, resulting in an increased density of the doublons in the core region compared to the initial state. As a main result, we show that this phenomenon is not limited to chains that were previously studied. Interestingly, there are additional dynamical processes on the two-leg ladder such as density oscillations and selftrapping of defects that lead to a less efficient distillation process. Initial product states are also considered, since in optical lattice experiments such states are often used as the initial setup. I propose configurations that lead to a fast and efficient quantum distillation.

Spin-orbit coupling exists in materials in general. However, it entangles the spin and orbital degrees of freedom and complicates the model. Thus, theorists usually neglect the effects induced by spin-orbit coupling first and consider spin-orbit coupling as perturbation next. The non-perturbative effects brought up by spin-orbit coupling are thus often less studied or overlooked. On the other hand, the majority in the study of interacting topological order focusing on the mathematical structure of theories and made significant advances by leaving material details behind. It is thus important to find possible microscopic models that could realize the new phases in laboratories and benefits from the progress of theories to make experimental predictions. In this talk, I will discuss the physical effects due to strong spin-orbit coupling from the perspective of searching new quantum orders and the non-trivial responses. We found a physical mechanism that realizes interesting models which can have non-trivial long range entangled phases in both 3D pyrochlore lattice and 2D Kagome lattice under different physical conditions. The 3D model can realize two distinct quantum spin ice phases, i.e. dipolar and octupolar quantum spin ices. The 2D model can realize a Z2 topological order with nontrivial symmetry fractionalization pattern. The particular Z2 topological order can be detected numerically or experimentally by the "vison zero modes" which is a remarkable topological signature induced by the onsite Ising symmetry and the space group symmetry. References: Yi-Ping Huang*, Gang Chen and Michael Hermele, PRL 112, 167203 (2014) Yi-Ping Huang* and Michael Hermele, PRB 95, 075130 (2017)

$\alpha$-RuCl$_3$ and Na$_2$IrO$_3$ are Mott insulators in the regime of strong spin-orbit coupling. When subject to an external magnetic field, $\alpha$-RuCl$_3$ has recently been proposed to realize a field-induced quantum spin liquid ground state. We will describe and explain the behavior of extended Heisenberg-Kitaev spin models, relevant for these materials, in a magnetic field. Broken SU(2) spin symmetry renders the magnetization processes rather complex, with sequences of nontrivial intermediate phases characterized by large unit cells and multiple or incommensurate ordering wavevectors. We discuss these findings in light of the recent experiments. References: [1] L. Janssen, E. C. Andrade, and M. Vojta, arXiv:1706.05380. [2] L. Janssen, E. C. Andrade, and M. Vojta, Phys. Rev. Lett. 117, 277202 (2016). [3] A. U. B. Wolter, L. T. Corredor, L. Janssen, K. Nenkov, S. Schönecker, S.-H. Do, K.-Y. Choi, R. Albrecht, J. Hunger, T. Doert, M. Vojta, and B. Büchner, Phys. Rev. B 96, 041405(R) (2017).

A repulsive Hubbard model with both spin-asymmetric hopping $(t_\uparrow\neq t_\downarrow)$ and a staggered potential (of strength $\Delta$) is studied in one dimension. The model is a compound of the "mass-imbalanced" $(t_\uparrow\neq t_\downarrow$, $\Delta=0)$ and "ionic" $(t_\uparrow\neq t_\downarrow$, $\Delta>0)$ Hubbard models, and may be realized by cold atoms in engineered optical lattices. We determine the phases and phase transitions in the ground state for a half-filled band. We find that a period-two modulation of the particle (or charge) density and an alternating spin density coexist for arbitrary $U\ge 0$. The amplitude of the charge modulation is largest at $U=0$, decreases with increasing $U$ and tends to zero for $U\rightarrow\infty$. The amplitude for spin alternation vanishes for $U=0$, increases with $U$ and tends to saturation for $U\rightarrow\infty$. Charge order dominates below a critical value $U_c$, whereas magnetic order dominates above. The mean-field Hamiltonian has two gap parameters, $\Delta_\uparrow$ and $\Delta_\downarrow$, which have to be determined self-consistently. For $U < U_c$ both parameters are positive, for $U > U_c$ they have different signs, and for $U=U_c$ one gap parameter jumps from a positive to a negative value. The weakly first-order phase transition at $U_c$ can be interpreted in terms of an avoided criticality (or metallicity). The system is reluctant to restore a symmetry that has been broken explicitly.

We consider the orthogonality catastrophe at the Anderson Metal-Insulator transition (AMIT). The typical overlap F between the ground state of a Fermi liquid and the one of the same system with an added potential impurity is found to decay at the AMIT exponentially with system size L as F ∼ exp($−cL^η$), where η is the power of multifractal intensity correlations. Thus, strong disorder typically increases the sensitivity of a system to an added impurity exponentially. We recover on the metallic side of the transition Anderson's result that fidelity F decays with a power law F ∼ $L^{−q(E_{F})}$ with system size L. Its power increases as Fermi energy $E_F$ approaches mobility edge $E_M$. On the insulating side of the transition F is constant for system sizes exceeding localization length ξ. While these results are obtained for the typical fidelity F, we find that log F has at large values a wide log normal tail, with a width diverging at the AMIT. S. K. Phys. Rev. Lett. 117,146602 (2016)

In recent years growing attention has been given to excited eigenstates of many-body systems and the question to what extent they differ from thermal states. However, accessing excited states in an interacting model is in general exponentially difficult and thus only achievable in small systems or very specific models. We show that the time-dependent formulation of the functional renormalization group can be extended to directly access excited eigenstates for a wide range of models. The resulting algorithm scales polynomially in the system size and is accurate for small to intermediate interactions. We use this method to investigate the physics of excited states of large tight-binding chains with nearest neighbor interaction and compare the observed behavior with the well understood phenomenology of an one dimensional metal at finite temperature.

To explore the static properties of the one-dimensional anyon-Hubbard model, we apply perturbation theory with respect to the ratio between kinetic energy and interaction energy in the Mott insulating phase. The strong-coupling results for the ground-state energy, the single-particle excitation energies, and the momentum distribution functions are benchmarked against the numerically exact (infinite) density-matrix renormalization group technique. Since these analytic expressions are valid for any fractional phase $\theta$ of anyons, they will be of great value for a sufficiently reliable analysis of future experiments, avoiding extensive and costly numerical simulations.

Fractionalization of elementary excitations remains an excotic phenomenon usually limited to 1D and 2D systems. Here we report spectroscopic signatures of fractional excitations in the 3D harmonic-honeycomb iridates beta - and gamma-Li2IrO3 [1]. Our experimental evidence is based on Raman spectroscopic investigations of the polarization and temperature dependence of a scattering continuum, a comparison with earlier investigations of alpha-RuCl3 [2], and a comparison with theoretical modelling of the Kitatev model on different topologies [3]. [1] A. Glamazda, P. Lemmens, S.-H. Do, K.-Y. Choi, Nature Commun. 7, 12286 (2016). [2] L. J. Sandilands, Y. Tian, K. W. Plumb, Y. -J. Kim, and K. S. Burch, PRL 114, 147201 (2015). [3] J. Knolle, G.-W. Chern, D. L. Kovrizhin, R. Moessner, and N. B. Perkins, PRL 113, 187201 (2014). B. Perreault, J. Knolle, N. B. Perkins, and F. J. Burnell, PRB 92, 094439 (2015). We acknowledge support by KRF 2009-0076079, GIF 1171-486 189.14/2011, NTH-CiN, and DFG-RTG 1952/1.

We reinvestigate the momentum-resolved single-particle spectral function of the Tomonaga-Luttinger model. In particular, we focus on the role of the momentum dependence of the two-particle interaction V(q) . Since this is irrelevant in the renormalization group sense, usually V(q) is assumed to be constant. However, certain momentum integrals arising in the analytic expressions for correlation functions then become ultraviolet divergent and have to be regularized with an ad hoc procedure. This does not affect universal low-energy properties, e.g. exponents of power laws, as long as all energy scales are sent to zero. If the momentum is fixed away from k_F , |k-k_F| sets a finite energy scale and the details of V(q) start to matter. In particular, it was shown in [1] that the flatness of V(q) at vanishing momentum plays an important role. Using a method to calculate the momentum-resolved spectral function which is based on [2], we provide strong evidence that any curvature of the two-particle interaction at small transferred momentum q destroys the power-law scaling at |k-k_F|>0 obtained with analytical methods employing the ad hoc procedure. Even for |k-k_F| much smaller than the momentum-space range of the interaction the spectral line shape depends on the details of V(q) . References: [1] V. Meden, Phys. Rev. B 60, 4571 (1999) [2] K. Schönhammer and V. Meden, Phys. Rev. B 47, 16205 (1993) [3] L. Markhof and V. Meden, Phys. Rev. B 93, 085108 (2016)

We present an extensive inelastic neutron scattering study of the dimerized quantum magnet SrCu2(BO3)2 (SCBO) with the goal of examining a recent proposal that the triplon modes in this material have nontrivial Chern numbers in applied magnetic field [1]. In addition to unprecedented resolution of the low field evolution of the single triplon intensity, the experiment reveals a novel feature: a dispersive mode at low energies that we interpret as a bound state in the singlet sector which is related to the proximity of SCBO to a quantum phase transition. Including interactions in the description of the triplons allows us to account theoretically for the available experimental data and make detailed predictions of a thermal Hall signature and chiral edge modes. [1] J. Romhanyi, R. Ganesh, K. Penc, Nat. Commun. 6, 6805 (2015). [2] P. McClarty et al. Nature Physics (2017) doi:10.1038/nphys4117

Heisenberg magnets on highly frustrated lattices are in the focus of theoretical studies. While there are numerous studies of the ground state, much less is known about the thermodynamic properties. We use the spin-rotation invariant Green's function method [1,2,3] as well as the high-temperature expansion up to order 13 [4] to study the temperature dependence of the magnetic structure factor $S_{\mathbf{Q}}$, the uniform susceptiblity $\chi_0$, the specific heat $C_V$, the correlation length $\xi_{\mathbf{Q}}$ and the correlation functions $\langle S_0S_{\mathbf{R}}\rangle$ for $S\ge1/2$ of the Heisenberg AFM on the kagome and pyrochlore lattices as well as the Heisenberg ferromagnet on the pyrochlore lattice for arbitray spin quantum number $S$. [1] B. H. Bernhard, B. Canals, and C. Lacroix, Phys. Rev. B $\textbf{66}$, 104424, (2002). [2] P. Müller, J. Richter, and D. Ihle, Phys. Rev. B $\textbf{95}$, 134407, (2017). [3] P. Müller, A. Lohmann, J. Richter, O. Menchyshyn, O. Derzhko, arXiv:1707.01529 [cond-mat.str-el], (2017). [4] A. Lohmann, H.-J. Schmidt, and J. Richter, Phys. Rev. B $\textbf{89}$, 014415, (2014).

The defining problem in the field of frustrated quantum magnetism is the ground state of the nearest-neighbour S = 1/2 antiferromagnetic Heisenberg model on the kagome lattice. Despite the simplicity of the Hamiltonian, the solution has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states (TNS), specifically the method of projected entangled simplex states (PESS), whose combination of a correct accounting for multipartite entanglement and infinite system size provides qualitatively new insight. By studying the ground-state energy, the staggered magnetization we find at all finite tensor bond dimensions and the effects of a second-neighbour coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of the gapless ground state.

We study the entanglement properties for a bipartition of the one-dimensional Hubbard model. By means of a recently-developed Quantum Monte Carlo method which exploits the replica trick [1], we sample the correlations of the entanglement Hamiltonian, and compare our results with those for an open chain of the same size of the entanglement cut. Ref. [1] F. F. Assaad, T. C. Lang, F. Parisen Toldin, Phys. Rev. B 89, 125121 (2014)

We numerically study the spin-$1/2$ breathing kagome lattice. In this variation of the kagome Heisenberg antiferromagnet, the spins belonging to upward and downward facing triangles have different coupling strengths. This type of anisotropy is particularly interesting because it fully preserves the frustration of the original model. Using the density matrix renormalization group (DMRG) method and exact diagonalization, we show that the kagome antiferromagnet spin liquid is extremely robust to this anisotropy. Materials featuring this anisotropy -- and especially the recently studied vanadium compound $[{\mathrm{NH}}_{4}{]}_{2}[{\mathbf{C}}_{7}{\mathbf{H}}_{14}\mathbf{N}][{\mathbf{V}}_{7}{\mathbf{O}}_{6}{\mathbf{F}}_{18}]$ (DQVOF) -- may thus be very good candidates to realize the much studied kagome spin liquid. Further, we closely examine the limit of strong breathing anisotropy and find indications of a transition to a nematic phase. Beyond its experimental implications, our work could also lead to interesting insight on the kagome spin liquid through the understanding of this phase transition. Ref: arxiv:1706.10105 C. Repellin, Y.C. He, F. Pollmann

We study geometrically frustrated spin systems coupled to fermions using quantum Monte Carlo simulations. The model considered is the honeycomb Kondo lattice model that spins including geometrical frustration and fermions interact via a Kondo coupling. Based on exact quantum Monte Carlo data, the phase diagram where geometrical frustration is an axis in addition to a Kondo coupling is obtained from finite-size scaling. We find that the macroscopic degeneracy of geometrically frustrated spins is lifted by a Kondo coupling and a three-sublattice magnetic ordered state emerges where the local moments are screened depending on site, in addition to an antiferromagnetic ordered and a Kondo screening states.

Disorder effects are especially pronounced around nodal points in linearly dispersing bandstructures as present in graphene or Weyl semimetals. Despite the enormous experimental and numerical progress, even a simple quantity like the average density of states cannot be assessed quantitatively by analytical means. We demonstrate how this important problem can be solved employing the functional renormalization group method and, for the two dimensional case, demonstrate excellent agreement with reference data from numerical simulations based on tight-binding models. In three dimensions our analytic results also improve drastically on existing approaches.

We use the variational cluster approximation to investigate the phase diagram and one-particle spectral density of multi-band Hubbard models with strong spin-orbit coupling. The approach includes quantum fluctuations on a small cluster exactly, where frustration can be treated without additional complications, and long-range order on a mean-field level. We will in particular investigate the filling of five electrons in the $t_{2g}$ subshell, as is realized in some iridium compounds. We present the phase diagram resulting from the competition of Hund′s rule and spin-orbit coupling with crystal-field splitting. We also present first insights into systems with four electrons per site, where a local singlet competes with itinerant triplet excitations that can condense into magnetic order.

A. Bohrdt^1, S. Eggert^2, K. Jägering^2, P. Matveeva^2, and I. Schneider^2 1) Department of Physics and Walter Schottky Institute, Technical University of Munich, 85748 Garching, Germany 2) Department of Physics and Research Center Optimas, Technical University of Kaiserslautern, 67663 Kaiserslautern, Germany Inelastic neutron scattering experiments on weakly doped quasi one-dimensional spin chain compounds have found a surprising enhancement of the spectral weight at low energies at the antiferromagnetic point as compared to the pure samples. In a simple model we take the weak disorder into account as an effective fragmentation of the spin chains. We obtain the momentum-resolved spectral weight for the finite segments at low-lying energies exactly using the density-matrix renormalization group algorithm. The numerical data are compared to bosonization results for scattering wave-vectors k≈π where we have identified the impurity contribution to the spin dynamics in a systematic finite-size scaling analysis. Summing up contributions of the distribution of finite length segments we obtain the overall result which we analyze in detail. For the isotropic chain additional logarithmic corrections to the correlations due to the bulk marginal operator are present. We consider the impact of these on the boundary behaviour for various one-dimensional models.

Spin ice is a geometrically frustrated system with a highly degenerate classical ground state manifold supporting monopole excitations. Large quantum fluctuations may permit tunnelling between spin ice configurations, leading to a quantum liquid state described by the Maxwell action of quantum electrodynamics. Here we discuss some of the new phenomena which result from interactions removing the degeneracy of spin ice configurations. Using Monte Carlo simulation methods we investigate the stability of the quantum liquid phase against ordered "chain states" in a realistic model of spin ice including long range dipolar interactions [1]. We also explore an effective model of spin ice with short range exchange interactions by examining the nature of spin ordered states in an external magnetic field. [1] P. McClarty, O. Sikora et al., Phys. Rev. B 92, 094418 (2015)

Correlations in quantum systems can be much stronger than in classical ones, an important manifestation of this is quantum entanglement. States of a bipartite system (pure or mixed) can be either uncorrelated or correlated, while for multipartite systems many different kinds of correlations arise. In the poster, (i) it is shown how to grasp this complicated structure efficiently, (ii) proper correlation measures are defined, (iii) the multipartite correlation based clustering of the system is mentioned, and (iv) the results of an algorithm for this clustering are shown. The importance of the latter two points is that the existence of higher correlations makes the bipartite correlation based ("graph theoretical") clustering insufficient. Also (v) the multipartite correlation theory is illustrated by showing examples from molecular physics. This field provides an excellent playground for multipartite correlation theory, since here the ground states of the many-body interacting Hamiltonians are naturally factorized into approximate products of clusters of localized orbitals. References: Phys. Rev. A 92, 042329 (2015) (arXiv:1503.06071 [quant-ph]) Sci. Rep. 7, 2237 (2017) (arXiv:1605.06919 [quant-ph])

We consider a system consisting of several correlated monoatomic layers sandwiched between two metallic leads. In addition to the local Hubbard interaction we also take the long-range Coulomb interaction into account, which causes electronic charge reconstruction in the correlated layers, as well as in the leads. The non-equilibrium situation is driven by applying a bias-voltage to the leads. We investigate the steady-state behavior of the system for different parameters (bias voltage, interaction strength, hybridization strength between leads and the correlated heterostructure). In particular, we present results for the steady-state current, spectral functions, and electronic charge reconstruction. Depending on the particular parameters we either observe a capacitor-like behavior or one dominated by charge transport. Furthermore, the Hubbard interaction has significant effect on the charge reconstruction. In order to investigate steady-state properties we use real-space Dynamical mean-field theory (R-DMFT) [1,2] combined with the Poisson equation, both solved in a self-consistent fashion. To account for the charge reconstruction in the leads we include some lead layers explicitly in R-DMFT in addition to the correlated layers. As impurity solver for R-DMFT we use the recently developed auxiliary master equation approach, which addresses the DMFT impurity problem within an auxiliary system consisting of a correlated impurity, a small number of uncorrelated bath sites and two Markovian environments described by a generalized Master equation [3-6]. References: [1] I. Titvinidze et al., Phys. Rev. B 94, 245142 (2016)\\ [2] J. K. Freericks, Phys. Rev. B 70, 195342 (2004) \\ [3] E. Arrigoni et al., Phys, Rev. Lett. 110, 086403 (2013)\\ [4] A. Dorda et al., Phys. Rev. B 89, 165105 (2014)\\ [5] I. Titvinidze et al., Phys. Rev. B 92, 245125 (2015) \\ [6] A. Dorda et al., arXiv:1608.04632 (2016)

We construct a many-body theory of magnetoelasticity in one dimension and show that the dynamical correlation functions of the quantum magnet, connecting the spins with phonons, involve all energy scales. Accounting for all magnetic states non-perturbatively via the exact diagonalisation techniques of Bethe ansatz, we find that the renormalisation of the phonon velocity is a non-monotonous function of the external magnetic field and identify a new mechanism for attenuation of phonons - via hybridisation with the continuum of excitations at high energy. We conduct ultrasonic measurements on a high-quality single crystal of the spin-1/2 Heisenberg antiferromagnet $Cs_2CuCl_4$ in its one-dimensional regime and confirm the theoretical predictions, demonstrating that ultrasound can be used as a powerful probe of strong correlations in one dimension.

Raman spectroscopy has become an invaluable tool to characterize the magnetic excitation spectrum of solids. The possibility to uncover fractional spinon excitations in quantum spin liquids [1,2] and Majorana fermions in Kitaev systems [3] is of particular relevance. Here we present the magnetic excitation spectrum of the quasi-1D Haldane chain compound $SrNi_2V_2O_8$ [4] probed via Raman spectroscopy. We observe a broad scattering continuum perpendicular to the chain direction. Its temperature dependence evidences fractional excitations of the symmetry protected topological Haldane phase as the origin of this continuum. As a characteristic energy we derive the Haldane gap from its temperature dependence. [1] D. Wulferding, P. Lemmens, P. Scheib, J. Röder, P. Mendels, S. Chu, T. Han, and Y. S. Lee, Phys. Rev. B 82, 144412 (2010). [2] V. Gnezdilov, P. Lemmens, Y. G. Pashkevich, D. Wulferding. I. V. Morozov, O. S. Volkova, and A. Vasiliev, Phys. Rev. B 85, 214403 (2012). [3] A. Glamazda, P. Lemmens, S.-H. Do, Y. S. Choi, and K.-Y. Choi, Nat. Commun. 7, 12286 (2016). [4] A. K. Bera and S. M. Yusuf, Phys. Rev. B 86, 024408 (2012).

We use quantum Monte-Carlo simulations to study an extended Hubbard model of hardcore bosons on the kagome lattice. In the limit of strong nearest-neighbor interactions at one-third filling, the interplay between frustration and quantum fluctuations leads to a valence bond solid ground state. The system undergoes a quantum phase transition to a superfluid phase as the interaction strength is decreased. It is still under debate whether the transition is weakly first order or represents an unconventional continuous phase transition. Utilizing large scale quantum Monte-Carlo simulations with parallel tempering in the canonical ensemble we find the phase transition appears to be continuous at exactly 1/3 filling. A careful finite size scaling analysis reveals an unconventional scaling behavior hinting at deconfined quantum criticality. We demonstrate that the system at 1/3 filling can be effectively described by the easy-plane NCCP$^1$ gauge theory.