# Korrelationstage 2019

For each poster contribution there will be one poster wall (width: 97 cm, height: 250 cm) available. Please do not feel obliged to fill the whole space. Posters can be put up for the full duration of the event.

### Non-equilibrium spin dynamics in periodically pumped quantum dots

Anders, Frithjof

Periodic laser pulsing of singly charged semiconductor quantum dots in an external magnetic field leads to a synchronization of the spin dynamics with the optical excitation. The pumped electron spins partially rephase prior to each laser pulse, causing a revival of electron spin polarization with its maximum at the incidence time of a laser pulse. The amplitude of this revival is amplified by the frequency focusing of the surrounding nuclear spins. I will present a fully quantum mechanical theory and an semi-classical approach for simulating up to 20 million laser pulses that are able to bridge between 11 orders of magnitude in time. We will discuss the resonant condition that leads to a non-monotonic dependency of the revival amplitude as function of the external field. We will discuss how slightly off-resonance pumping does effect the dephasing time in a periodically pumped quantum dot ensemble and show strong evidence that there is an intrinsic long range interaction between the electron spins of a quantum dot ensemble of still unknown microscopic origin that might be generated by an RKKY mechanism.

### Nonequilibrium transport in correlated impurities and photovoltaics

Arrigoni, Enrico

I will present recent developments of the so-called Auxiliary Master Equation Approach (AMEA) to deal with correlated quantum impurities out of equilibrium. This method combining nonequilibrium Green's functions and Lindblad-Master equation schemes [1,2,3] yelds accurate results down to the Kondo scale and can be used as an effective impurity solver within nonequilibrium Dynamical Mean Field Theory [4]. In AMEA the "physical" impurity problem is replaced by an auxiliary open quantum system including bath orbitals as well as a coupling to a Markovian environment. The mapping becomes exponentially exact upon increasing the number of bath orbitals. The auxiliary open quantum system is then solved by (non-hermitian) Lanczos exact diagonalisation [2], matrix-product states (MPS) [3], or by stochastic wave function approaches [5] I will discuss photoexcitation induced transport across a Mott insulating gap in connection with the of issue of impact ionization [4]. Transport and spectral properties of selected quantum impurity models out of equilibrium will also be presented [3,5]. [1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013) [2] A. Dorda et al., Phys. Rev. B 89 165105 (2014) [3] A. Dorda et al., Phys. Rev. B 92, 125145 (2015); [4] M. Sorantin et al., Phys. Rev. B 97, 115113 (2018) [5] M. Sorantin et al., Phys. Rev. B 99, 075139 (2019)

### The ALF (Algorithms for Lattice Fermions) open source project

The Algorithms for Lattice Fermions package [1] provides a general code for the finite temperature and projective auxiliary field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to an Ising or scalar field with given dynamics. We provide predefined types that allow the user to specify the model, the Bravais lattice as well as equal time and time displaced observables. The code supports an MPI implementation. Examples such as the Hubbard model on the honeycomb lattice and the Hubbard model on the square lattice coupled to a transverse Ising field are provided and discussed in the documentation. We furthermore discuss how to use the package to implement the Kondo lattice model and the SU(N)-Hubbard-Heisenberg model. [1] M. Bercx, F. Goth, J. S. Hofmann, and F. F. Assaad, “The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code,” SciPost Phys., vol. 3, p. 013, 2017.

### Practical quantum advantage of dynamical structure factors in analogue quantum simulations

Baez, Maria Laura

The dynamical structure factor is one of the prime experimental quantities crucial in scrutinising the validity of the microscopic description of strongly correlated systems. However, despite its long-standing importance, it is exceedingly difficult in generic cases to numerically calculate it, ensuring that the necessary approximations involved yield a correct result. Acknowledging this practical difficulty consider how analogue quantum simulators can offer a computational speed-up over classical algorithms. We elaborate on a novel, readily available, measurement set-up allowing for the determination of the dynamical structure factor on different architectures, including arrays of ultra-cold atoms, trapped ions, Rydberg atoms, and superconducting qubit chips. We go on to study the dynamical structure factor in the presence of typical experimental imperfections, and show an inherent robustness for the particular cases of the short and long range transverse field Ising models. Our numerical results suggest that quantum simulations employing these near-term noisy intermediate scale quantum devices should allow for the observation of the characteristic features of the dynamical structure factor of correlated quantum matter, even in the presence of current experimental imperfections, and for larger system sizes than what is currently achievable by classical simulation techniques. We then turn to identifying the computational complexity of this task, linking it to other standard problems in quantum simulation such as simulating out-of-equilibrium time evolution and quantum annealing, related to the complexity classes BQP and NP. With this work, we show that analogue quantum simulators can measure dynamical structure factors, and that the computational complexity of calculating this quantity belongs to the BQP-hard class, effectively exhibiting the prospect for demonstrating practical quantum advantages in the near term.

### The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model

Behrends, Jan

The Sachdev-Ye-Kitaev (SYK) model, in its simplest form, describes k Majorana fermions with random all-to-all four-body interactions. We consider the SYK model in the framework of a many-body Altland-Zirnbauer classification that sees the system as belonging to one of eight (real) symmetry classes depending on the value of $k \mod 8$. We show that, depending on the symmetry class, the system may support exact many-body zero modes with the symmetries also dictating whether these may have a nonzero contribution to Majorana fermions, i.e., single-particle weight. These zero modes appear in all but two of the symmetry classes. When present, they leave clear signatures in physical observables that go beyond the threefold (Wigner-Dyson) possibilities for level spacing statistics studied earlier. Signatures we discover include a zero-energy peak or hole in the single-particle spectral function, depending on whether symmetries allow or forbid zero modes to have single-particle weight. The zero modes are also shown to influence the many-body dynamics, where signatures include a nonzero long-time limit for the out-of-time-order correlation function. Furthermore, we show that the extension of the four-body SYK model by quadratic terms can be interpreted as realizing the remaining two complex symmetry classes; we thus demonstrate how the entire tenfold Altland-Zirnbauer classification may emerge in the SYK model.

### Quench Dynamics and Thermalization in Interacting Topological Systems

Budich, Jan Carl

We discuss the coherent non-equilibrium dynamics of interacting topological insulator systems after a quench from a trivial to a topological phase. While the many-body wavefunction is constrained to remain topologically trivial under local unitary evolution, we find that the Hall response of a quenched 2D system can dynamically approach a thermal value of the post-quench Hamiltonian, even though the efficiency of this thermalization process is shown to strongly depend on the microscopic form of the interactions. Quite remarkably, the effective temperature of the steady state Hall response can be arbitrarily tuned with the quench parameters. This behavior is reflected in a the single-particle density matrix which is found to dynamically undergo a topological transition before approaching a thermal state of the post-quench Hamiltonian. Our findings suggest a new way of inducing and observing low temperature topological phenomena in correlated ultracold atomic gases, where the considered quench scenarios can be realized in current experimental set-ups.

### Charge pumping along tailored paths in two-dimensional integer and fractional Chern insulators

Eckardt, André

The insertion of a local magnetic flux, as the one created by a thin solenoid, plays an important role in gedanken experiments of quantum Hall physics. I will present a proposal for the realization of such local solenoid-type magnetic fields in optical lattices, where Floquet engineering is combined with the ability of single-site addressing in quantum gas microscopes [1]. It will be shown that this technique can be used to realize (fractionally) quantized charge pumping along tailored paths in two-dimensional integer [1] and fractional [2] Chern insulators. [1] Floquet engineering of optical solenoids and quantized charge pumping along tailored paths in two-dimensional Chern insulators, B. Wang, F. N. Ünal, and A. Eckardt, Phys. Rev. Lett. 120, 243602 (2018) [2] Creating, probing, and manipulating fractionally charged excitations of fractional Chern insulators in optical lattices, M. Raciunas, F.N. Ünal, E. Anisimovas, and A. Eckardt, arXiv:1804.02002

### Overcoming the entanglement barrier in simulating long-time evolution

Eisert, Jens

Quantum many-body systems out of equilibrium pose some of the most intriguing questions in physics. Unfortunately, numerically keeping track of time evolution of states for strongly correlated models constitutes a severe challenge for all known methods. Prominently, tensor network methods are marred by an entanglement blowup, which allows to simulate systems following global quenches only to constant time. In this work, we take serious steps to achieve long-time simulation for interacting fermionic or equivalent spin systems, establishing the mindset that when keeping track of evolution in one-dimensional real space, an inappropriate subspace is being parametrized by matrix product states. In contrast, if the manifold reflecting both tensor network states and fermionic mode transformations is chosen, significantly longer times can be achieved. We argue that it is genuine correlations between modes and not real-space entanglement that is the actual limiting factor. Equipped with this new tool, we explore the physics of equilibration, pre-thermalization and thermalization [1]. If time allows, other recent developments to capture natural higher-dimensional systems with tensor networks will be discussed, such as new algorithms to capture thermal [2] and double-layered strongly correlated systems encountered in the laboratory and featuring novel frustration mechanisms [3]. [1] C. Krumnow, J. Eisert, O. Legeza, in preparation (2019). [2] A. Kshetrimayum, M. Rizzi, J. Eisert, R. Orus, arXiv:1809.08258 (2018). [3] A. Kshetrimayum, B. Lake, A. Nietner, J. Eisert, in preparation (2019).

### Suppression of the Hall Response by the Topology of the Fermi Surface

Filippone, Michele

We demonstrate the identical suppression of the Hall response ($\sigma_{\rm H}\equiv0$) in quasi two-dimensional ballistic lattices. This suppression is robust to relatively large variations of magnetic field, Fermi level, interactions, temperature, disorder and absence of particle-hole symmetry. This suppression is totally unexpected and we show its relation to the topological properties of the Fermi surface: namely its central charge. We show that these out-of-equilibrium states are commonly realized in standard (Landauer) quantum transport settings and we rely on DMRG to show that our results equally apply to strongly interacting regimes. Our results unveil novel robust and experimentally measurable properties of quantum coherent transport phenomena in the presence of gauge fields.

### Relaxation in classical integrable systems

Gamayun, Oleksandr

I will consider non-equilibrium dynamics in the classical integrable systems. The integrability manifests itself in an analog of the Eigenstate State Thermalization Hypothesis, which allows finding the exact form the large time asymptotic profile. I will describe relaxation dynamics in one-dimensional Bose gases, formulated as an initial value problem for the classical nonlinear Schrodinger equation, as well as domain wall "melting " in XXZ magnetic.

### Dynamical topological quantum phase transitions in nonintegrable models

Hagymási, Imre

We consider sudden quenches across quantum phase transitions in the spin-1 XXZ model with single-ion-type anisotropy, where the initial state is a symmetry-protected topological phase and the ground state of the final Hamiltonian has no topological order. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in the rate function for the return probability. In addition, we show that the temporal behavior of the string order parameter is intimately related to the subsequent dynamical phase transitions. Using the tools of quantum information we reveal the intrinsic entanglement structure of the time-evolved states and point out that in certain cases the dynamical quantum phase transitions are accompanied by enhanced two-site entanglement.

### Dynamical quantum phase transitions

Heyl, Markus

Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to quantum states with novel properties of genuine nonequilibrium nature. However, for the theoretical description it is in general not sufficient to understand nonequilibrium dynamics on the basis of the properties of the involved Hamiltonians. Instead it becomes important to characterize time-evolution operators which adds time as an additional scale to the problem. In this talk I will summarize recent progress in the field of dynamical quantum phase transitions, which are phase transitions in time with temporal nonanalyticities in matrix elements of the time-evolution operator. These transitions are therefore not driven by an external control parameter, but rather occur due to sharp internal changes generated solely by unitary real-time dynamics. I will discuss obtained insights on general properties of dynamical quantum phase transitions, their physical interpretation, as well as recent experimental observations.

### Multiloop functional renormalization group for response functions

Hille, Cornelia

We present a functional renormalization group (fRG) study of the two dimensional Hubbard model, which includes the recently introduced multiloop extension that allows to sum up all diagrams of the parquet approximation with their exact weight. Due to its iterative structure based on successive one-loop computations, the loop convergence of the fRG results can be obtained with an affordable numerical effort. Together with an efficient parametrization of the two particle vertex, this fRG-based computation scheme paves the route towards quantitative analyses in different parameter regimes and predictions for more challenging systems.

### Phase Diagram of a Spin-Orbital Model for Twisted Bilayer Graphene

Hisano Natori, Willian Massashi

Twisted bilayer graphene (TBG) systems have attracted widespread attention since the discovery of their unusual Mott- and superconductor behavior at specific twist angles. Several theoretical approaches to explain the correlation mechanisms in TBG were proposed. One of them is to study them through minimal spin-orbital models. Their local degrees of freedom are doubly degenerate Wannier orbitals derived from ab initio calculations that are located on a moiré honeycomb lattice. Here, we analyze a model developed for TBG at quarter- filling that includes the effects of Hund’s coupling and bond-dependent hopping terms. This is an example of Kugel-Khomskii model that often is used to describe the magnetism of transition metal compounds. We combine Variational Monte Carlo (VMC) and linear flavor- wave theory (LFWT) computations to argue in favor of a quantum spin- orbital liquid (QSOL) over a large area of the phase diagram. VMC also indicates the absence of a transition to valence crystal (VC) phases.

### Interchain mean-field theory for the bimetallic ferromagnetic spin-chain compound MnNi(NO$_2$)$_4$(en)$_2$ (en = ethylenediamine)

Honecker, Andreas

MnNi(NO$_2$)$_4$(en)$_2$, en = ethylenediamine contains ferromagnetically coupled chains with alternating spins of magnitude 5/2 and 1. Two peak-like structures are observed in the field-dependent specific heat of this compound. This behavior is attributed to the existence of two modes in the spin-wave dispersion. Here we present numerical results for the specific heat obtained by exact diagonalization and Quantum-Monte-Carlo simulations for the alternating spin-chain model, using parameters that have previously been derived from the high-temperature behavior of the magnetic susceptibility. MnNi(NO$_2$)$_4$(en)$_2$ orders antiferromagnetically at low temperatures in zero magnetic field, demonstrating relevant antiferromagnetic interchain coupling. We therefore develop an interchain mean-field approach: the magnetization of a chain generates an effective magnetic field on the neighboring chains that is computed self-consistently. In addition to this renormalization of the magnetic field, we derive and evaluate corrections to the specific heat arising from interchain coupling. In this manner we obtain a surprisingly accurate description of the three-dimensional ordering transition of MnNi(NO$_2$)$_4$(en)$_2$ based on Quantum-Monte-Carlo simulations of individual chains. The antiferromagnetically ordered state of MnNi(NO$_2$)$_4$(en)$_2$ is suppressed already by a weak magnetic field. This observed strong effect of an applied magnetic on the ordered state and in particular the specific heat promises interesting magnetocaloric properties that we discuss from a theoretical perspective.

### to be announced

Karrasch, Christoph

### Combining the functional renormalization group with the density functional theory for realistic two dimensional materials

Khedri, Andisheh

We employ a combination of the functional renormalization group (FRG) and the density functional theory (DFT) to compute the phase diagram of realistic materials. We focus on the multi-band two dimensional Hubbard model with the effective parameters obtained from the DFT, i.e., the hopping and Coulomb matrix elements, and we investigate the signatures of many-body interactions with the FRG method. We revisit the twisted bilayer graphene, and we study different ordering tendencies, from superconductivity to antiferromagnetic insulating behavior. We provide a qualitative comparison to the recent experiments and various theoretical attempts to explain them.

### Revisiting cellular dynamical mean-field theory on the two-particle level

Klett, Marcel

Using the cellular dynamical mean-field theory (CDMFT) we study both single-particle and two-particle quantities of the two-dimensional Hubbard model at half-filling. A newly developed continuous time quantum Monte-Carlo impurity solver allows us to go reach cluster sizes up to N = 81 sites, and to assess the impact of the cluster size on the physical observables. In particular, for the spectral function we find a substantial reduction of the critical interaction value where a Mott like metal-insulator phase transition appears with increasing cluster size. We further compute the two-particle spin susceptibility and extract the corresponding correlation length from its decay in real space. We observe a divergent behavior in proximity of the phase transition line between the ordered antiferromagnetic and a disordered paramagentic phase induced by the finite cluster sizes.

### Poor man's scaling and Lie algebras

Kogan, Eugene

We consider a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, derive the scaling equation and analyse the connection between its explicit form and the symmetry of interaction. On the basis of this analysis we write down explicitly the scaling equation for the case when the interaction is written in terms of $su(3)$ generators but has a symmetry described either by $SU(2)$ or by $SU(2)\times U(1)$ group.

### Orbital differentiation in Hund metals

Kugler, Fabian

Orbital differentiation is a common theme in multi-orbital systems, yet a complete understanding of it is still missing. Here, we focus on three-orbital Hubbard models to describe the $t_{2g}$ bands of materials such as ruthenates and iron-based superconductors, and provide results of unprecedented accuracy by using the numerical renormalization group as real-frequency impurity solver for dynamical mean-field theory. First, we consider a minimal model for orbital differentiation, where a crystal field shifts one orbital in energy, and describe the various phases with dynamic correlation functions. Upon approaching the orbital-selective Mott transition, we find a strongly suppressed spin-coherence scale and uncover the emergence of a singular Fermi liquid and interband doublon-holon excitations. Then, we apply our method to the paradigmatic material Sr$_2$RuO$_4$ in a real-materials framework. We illustrate distinctive Hund-metal features and provide theoretical evidence for a Fermi-liquid scale of about 25 Kelvin.

### Imaging the Wigner Crystal of Electrons in One Dimension

Legeza, Örs

The quantum crystal of electrons, predicted more than 80 years ago by Eugene Wigner, remains one of the most elusive states of matter. In this study, we observed the one-dimensional Wigner crystal directly by imaging its charge density in real space. To image, with minimal invasiveness, the many-body electronic density of a carbon nanotube, we used another nanotube as a scanning-charge perturbation. The images we obtained of a few electrons confined in one dimension match the theoretical predictions for strongly interacting crystals. The quantum nature of the crystal emerges in the observed collective tunneling through a potential barrier. These experiments provide the direct evidence for the formation of small Wigner crystals and open the way for studying other fragile interacting states by imaging their many-body density in real space.

### Twisted light - new perspectives to probe topological solids

Lemmens, Peter

Twisted light - new perspectives to probe topological solids Peter Lemmens, Florian Büscher, Dirk Wulferding IPKM, TU-BS, and LENA, TU-BS, Braunschweig, Germany We suggest “twisted light” to be a novel probe of topological degrees of freedom and nonlocal states. This unconventional light polarization with finite orbital angular momentum (OAM) is prepared using spatially modulated filters ("q-plates") [1,2]. It has previously been used, e.g. to control bound electron states in atomic physics [3] and been manipulated by meta-surfaces. In this presentation we will show experiments on systems with topological band structures and electronic density fluctuations. Work supported by QUANOMET NL-4, DFG LE967/16-1, and Quantum Frontiers. References: [1] Marrucci, et al., Phys. Rev. Lett. 96, 163905 (2006). [2] Slussarenko, et al., Opt. Express 19, 4085 (2011). [3] Schmiegelow, et al., Nat. Communications 7, 12998 (2016).

### Tensor network (iPEPS) study of the two-dimensional $t$-$J$ model

Li, Jheng-Wei

We study the ground states of the $t$-$J$ model on a square lattice in the thermodynamic limit using infinite projected infinite projected entangled pair states (iPEPS). At the underdoped region, multiple orders, such as spin density wave, charge density wave and $d$-wave paring have been suggested previously. However, the relation between different orders is yet to be understood. Here, we addresses this question using an iPEPS tensor network algorithm, both with and without exploiting the SU(2) spin symmetry. Also, the equal-time spin and charge correlations are computed to investigate their fluctuations in the real space. We find that at small doping region, $\delta\lesssim 0.2$, spin (magnetic) stripes are pinned by long-range antiferromagnetic order, and uniform $d$-wave paring is suppressed. This is consistent with the experimental case in La$_{\text{2-x}}$BaCuO$_{\text{4}}$ at $1/8$ doping. Close to optimal doping, $\delta \approx 0.2$, we observe the emergence of $d$-wave pairing using a SU(2) spin-invariant ansatz. Interestingly, a charge density wave associated with Fermi-surface instabilities also appears in this regime.

### Hidden phases in the photo-doped two-band Hubbard model

Li, Jiajun

Recent years have witnessed intense interest in controlling materials through non-equilibrium protocols. In particular, a strong electric pulse can drastically perturb a Mott insulator, giving rise to a transient photo-doped state featuring charge excitations across the insulating gap. This protocol of photo-doping can yield non-trivial physical consequences, such as non-thermal melting of symmetry-breaking phases and the formation of hidden states with intertwined spin-orbital ordering which is inaccessible in equilibrium. Using non-equilibrium Dynamical Mean-Field Theory, we identify a general electronic mechanism for the formation of hidden phases. We find the photo-induced charge excitations can gradually relax and transfer energy to spin and orbital orders at dramatically different paces in the sub-picoseconds time regime, leading to a highly non-thermal ordering [1]. Due to the limited time range of simulations for real-time dynamics, a theoretical understanding of photo-doped systems on the time scale from picoseconds to nanoseconds is still lacking. To systematically examine this regime, we adopt the steady-state formulation of Dynamical Mean-Field Theory to describe a long-lived photo-doped system, which is continuously perturbed to maintain a stationary state with charge excitations across the gap. Using this method, we study a photo-doped two-band Hubbard model. We find the photo-doping drives the system to a hidden phase, which exhibits non-thermal ordering essentially distinct from an equilibrium or Floquet engineered system.

### Hidden orders in frustrated magnets and their detection with an interpretable machine

Liu, Ke

Frustrated systems host myriads of exotic states of matter. These include various spin nematics and spin liquids. However, we usually lack an efficient way to discern them. Failing to do so will mislead the nature of the phase and the underlying physical law. In this talk, I will review some instances of hidden multipolar orders in frustrated magnets, and introduce a machine-learning method to detect their occurrence. This method exploits the theory of orientational tensor and the strong interpretability of support vector machines. It can extract intricate order parameters and to simultaneously identify multiple phase transitions, hence may act as a new scheme to explore unknown phase diagrams and as a comprehensive way to scrutinize spin liquid candidates.

### Investigating the roots of the nonlinear Luttinger liquid phenomenology

Meden, Volker

The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the dynamical structure factor of the interacting electron gas shows a logarithmic threshold singularity when evaluated to first order perturbation theory in the two-particle interaction. This term was interpreted as the linear one in an expansion which was conjectured to resum to a power law. A field theory, the mobile impurity model, which is constructed such that it provides the power law in the structure factor, was suggested to be the proper effective model and argued to form the basis of the nonlinear Luttinger liquid phenomenology. Surprisingly, the second order contribution was so far not computed. We close this gap and show that it is consistent with the conjectured power law. We take this as a motivation to critically assess the steps leading to the mobile impurity Hamiltonian. We, in particular, highlight that the model does not allow to include the effect of the momentum dependence of the (bulk) two-particle potential. This was recently shown to spoil power laws which so far were widely believed to be part of the Tomonaga-Luttinger liquid universality. This raises doubts that the conjectured nonlinear Luttinger liquid phenomenology can be considered as universal.

### One Proximate Kitaev Spin Liquid in the $K$-$J$-$\Gamma$ Model on the Honeycomb Lattice

Normand, Bruce

In addition to the Kitaev ($K$) interaction, candidate Kitaev materials also possess Heisenberg ($J$) and off-diagonal symmetric ($\Gamma$) couplings. We investigate the quantum ($S = 1/2$) $K$-$J$-$\Gamma$ model on the honeycomb lattice by a variational Monte Carlo (VMC) method. In addition to the generic' Kitaev spin liquid (KSL), we find that there is just one proximate KSL (PKSL) phase, while the rest of the phase diagram contains different magnetically ordered states. The PKSL is a gapless Z$_2$ state with 14 Majorana cones, which in contrast to the KSL has a gapless spin response. In a magnetic field applied normal to the honeycomb plane, it realizes two of Kitaev's gapped chiral spin-liquid phases, of which one is non-Abelian with Chern number $\nu = 5$ and the other is Abelian with $\nu = 4$. These two phases could be distinguished by their thermal Hall conductance.

### Numerically exact simulations of periodically-driven one-dimensional extended Hubbard model

Okamoto, Junichi

Floquet engineering using periodic driving in many-body systems offer a new route to realize novel model Hamiltonians. In cold atom systems, it has been used to control topology of a band structure [1], to create artificial gauge fields [2], and to change tunneling rate [3]. Here, we investigate a periodically driven one-dimensional extended Hubbard model with an exact time-dependent Schrödinger equation solver. We find that the rapid oscillation of external fields suppresses the tunneling rate, which leads to a transition from a gapless metallic phase to a gapped stripe phase. Time-dependent order parameters and transient conductivity are calculated to characterize the transition. We find that these quantities do not necessarily correspond to each other as in the equilibrium situations. Furthermore, two different definitions of transient conductivity give slightly different results. In general, overall behaviors are well captured by a Floquet effective Hamiltonian, while we also discuss cases when such a picture does not hold. [1] M. Tarnowski et al., Phys. Rev. Lett. 118, 240403 (2017) [2] J. Struck et al., Nature Physics 9, 738 (2013) [3] C. Sias et al., Phys. Rev. Lett. 100, 040404 (2008)

### Thermodynamic bootstrap program for dynamic correlation functions

Panfil, Miłosz

I will address the problem of computing dynamic correlation functions in Integrable QFT’s at finite temperature and out of equilibrium. The approach is based on the form-factor expansion of the correlation functions. Thanks to the integrability, the form-factors at finite temperature can be effectively bootstrapped, through a procedure generalising the Smirnov’s bootstrap program for vacuum form factors. The method allows to determine the dynamic correlation functions of strongly interacting systems. The talk is based on the work with A. C. Cubero (JHEP 104 (2019)) and forthcoming publications.

### Entanglement Hamiltonian of Interacting Fermionic Models

Parisen Toldin, Francesco

Recent numerical advances in the field of strongly correlated electron systems allow the calculation of the entanglement spectrum and entropies for interacting fermionic systems. An explicit determination of the entanglement (modular) Hamiltonian has proven to be a considerably more difficult problem, and only a few results are available. We introduce a technique to directly determine the entanglement Hamiltonian of interacting fermionic models by means of auxiliary field quantum Monte Carlo simulations. We implement our method on the one-dimensional Hubbard chain partitioned into two segments and on the Hubbard two-leg ladder partitioned into two chains. In both cases, we study the evolution of the entanglement Hamiltonian as a function of the physical temperature. Ref.: Francesco Parisen Toldin and Fakher F. Assaad, Phys. Rev. Lett. 121, 200602 (2018)

### Negative thermal expansion in the plateau state of a magnetically-frustrated spinel

Penc, Karlo

In this contribution, we report on the negative thermal expansion in the high–field, half–magnetization plateau phase of the frustrated magnetic insulator CdCr$_2$O$_4$. Using dilatometry, we precisely map the phase diagram at fields of up to 30 T, and identify a strong negative thermal expansion associated with the collinear half– magnetization plateau for B > 27 T. The resulting phase diagram is compared with a microscopic theory for spin-lattice coupling, and the origin of the thermal expansion is identified as a large negative change in magnetization with temperature, coming from a nearly–localised band of spin excitations in the plateau phase.

### Quantum oscillations in topological Kondo insulators

Peters, Robert

One of the most puzzling recent experimental discoveries in condensed matter physics has been the observation of quantum oscillations in insulating materials SmB6 and YbB12 [1,2]. Our understanding of quantum oscillations is rooted in the existence of a Fermi surface; electron bands, which form the Fermi surface, form Landau levels in a magnetic field. When the magnetic field strength is changed, the energy of these Landau levels changes which lead to an oscillatory behavior in almost all of the observable properties. However, SmB6 and YbB12 are strongly correlated f electron systems for which a gap develops due to hybridization between conduction electrons and strongly correlated f electrons, and thus a large resistivity at low temperatures can be measured. Thus, we can expect that SmB6 and YbB12 do not possess a Fermi surface, thus there are no electrons, which can form Landau levels close to the Fermi energy. On the other hand, SmB6 and YbB12 are both good candidates for topological Kondo insulator. Naturally, the question arises, if these quantum oscillations can be due to the interplay between non-trivial topology and strong correlations. We here answer this question by showing results of dynamical mean field theory in a magnetic field for two and three-dimensional models of topological Kondo insulators. We demonstrate that the gap closing, described for a noninteracting continuum model with momentum dependent hybridization [3], persists for a strongly correlated topological Kondo insulator on a lattice. Furthermore, we demonstrate that the amplitude of quantum oscillations is strongly enhanced due to correlations, which makes them easily observable in quantities like magnetization and resistivity over a wide range of magnetic fields before the magnetic breakdown occurs. [1] Tan et al. Science 349, 287 (2015) [2] Z. Xiang et al. in Science (2018) [3] Long Zhang et al. Phys. Rev. Lett. 116, 046404 (2016)

### Electrically tunable gauge fields in tiny-angle twisted bilayer graphene

Ramires Neves de Oliveira, Aline

Twisted bilayer graphene has recently attracted a lot of attention for its rich electronic properties and tunability. In particular, the discovery of Mott insulating regime and superconductivity in magic angle graphene superlattices ($\alpha \approx 1^\circ$) highlights the potential to realize tunable flat bands and strong correlations in pure graphene platforms. Here we show that for very small angles, $\alpha \ll 1^\circ$, the application of a perpendicular electric field is mathematically equivalent to a gauge field. This mapping allows us to predict the emergence of highly localized modes that are associated with flat bands close to charge neutrality, and whose energy can be tuned by the electric interlayer bias. Interestingly, the electrically generated localized modes closest to charge neutrality form an emergent Kagome lattice, in contrast to the triangular lattice formed by the flat bands at the magic angles. Our findings indicate that for tiny angles, biased twisted bilayer graphene is a promising platform which can realize frustrated lattices of highly localized states, opening a new direction for the investigation of strongly correlated phases of matter.

### Finite-size realization of the sawtooth spin chain close to quantum criticality

Richter, Johannes

Authors: J. Richter (MPIPKS), J. Schnack (Uni Bielefeld), D.V. Dmitriev and V. Ya. Krivnov (Institute of Biochemical Physics, Moscow) The Heisenberg model on the sawtooth (delta) chain is an example for a frustrated quantum spin system with a flat one-magnon band leading to a massively degenerate ground state and an unconventional low-temperature thermodynamics. For the well-studied sawtooth chain with antiferromagnetic (AFM) nearest-neighbor (NN) zigzag bonds J1 and AFM next-nearest-neighbor (NNN) basal bonds J2 [1-3] the flat band-physics emerges for J2=J1/2 near the saturation field, which, as a rule, is not easily accessible in experiments. By contrast, for the sawtooth chain with ferromagnetic (FM) J1 and AFM J2 [4,5] a zero-temperature transition between a ferro- and a ferrimagnetic ground state takes place at J2=-J1/2 and the flat band-physics is present at this point for zero magnetic field. At the transition point a class of exact many-body ground states formed by localized magnons can be found and the ground state is macroscopically degenerate with a large residual entropy per spin $s_0=\frac{1}{2}\ln 2$. Another important feature is a sharp decrease of the gaps for excited states with an increase of the number of magnons. These excitations give an essential contribution to the low-temperature thermodynamics. In the recently synthesized magnetic molecule [Fe10Gd10(Me-tea)10(Me-teaH)10(NO3)10 ]20MeCN (Fe10Gd10) the magnetic ions Fe ($S_{Fe}=5/2$) and Gd ($S_{Gd}=7/2$) form a sawtooth chain with a FM NN Fe-Gd coupling J1 and an AFM NNN Fe-Fe coupling J2, where the ratio of J2/J1 is close to the transition point [6]. As a consequence, the low-temperature physics of Fe10Gd10 is strongly influenced by the unusually high density of low-lying excitations stemming from the huge manifold of states becoming macroscopically degenerate at the transition point. Since these low-lying excitations belong to different magnetizations there is a strong impact of the magnetic field on the low-temperature properties of Fe10Gd10 [6]. In addition, to the study of the quantum model we also present an exact solution of the classical model relevant in the large-$S$ limit and discuss the role of quantum effects by considering the model for various spin $S$ [7]. [1] D. Sen, B.S. Shastry, R.E. Walsteadt and R. Cava, Phys. Rev. B 53 ,6401 (1996). [2] J. Schulenburg, A. Honecker, J. Schnack, J. Richter and H.J. Schmidt, Phys. Rev. Lett. 88, 167207 (2002). [3] O. Derzhko and J. Richter, Eur. Phys. J. B 52, 23 (2006). [4] V.Ya. Krivnov, D.V. Dmitriev, S. Nishimoto, S.-L. Drechsler and J.Richter, Phys. Rev. B 90, 014441 (2014). [5] D.V. Dmitriev and V. Ya. Krivnov, Phys. Rev. B 92 184422 (2015). [6] A. Baniodeh, N. Magnani, Y. Lan, G. Buth, C. E. Anson, J. Richter, M. Affronte, J. Schnack and A. K. Powell, npj Quantum Materials 3, 10 (2018) [7] D.V. Dmitriev, V. Ya. Krivnov, J. Schnack and J. Richter, in preparation.

### Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions

Richter, Jonas

We demonstrate that numerical linked cluster expansions (NLCE) yield a powerful approach to calculate time-dependent correlation functions for quantum many-body systems in one dimension. As a paradigmatic example, we study the dynamics of the spin current in the spin-1/2 XXZ chain for different values of anisotropy, as well as in the presence of an integrability-breaking next-nearest neighbor interaction. For short to intermediate time scales, we unveil that NLCE yields a convergence towards the thermodynamic limit already for small cluster sizes, which is much faster than in direct calculations of the autocorrelation function for systems with open or periodic boundary conditions. Most importantly, we show that the range of accessible cluster sizes in NLCE can be extended by evaluating the contributions of larger clusters by means of a pure-state approach based on the concept of dynamical quantum typicality (DQT). Even for moderate computational effort, this combination of DQT and NLCE provides a competitive alternative to existing state-of-the-art techniques, which may be applied in higher dimensions as well.

Rizzi, Matteo

### Superconductivity from Condensation of Topological Skyrmion Defects in Quantum Spin-Hall State

Sato, Toshihiro

We introduce a model of Dirac fermions in 2+1 dimensions that has the potential to dynamically generate quantum spin-Hall and superconductivity mass terms that permits negative-sign-free auxiliary-field quantum Monte Carlo simulations. We provide a realization of quantum spin-Hall state emerging from spontaneous SO(3) symmetry breaking. The corresponding SO(3) order parameter permits both long-wavelength Goldstone modes and topological skyrmion defects. The main finding is the observation of the continuous phase transition between quantum spin-Hall state and superconductivity. The mechanism for superconductivity from quantum spin-Hall state involves the condensation of skyrmion defects of quantum spin-Hall order parameter with charge 2e.

### Quantum dots under periodic pumping: spin inertia and nuclei-induced frequency focusing

Schering, Philipp

Quantum dots subjected to periodic pumping by optical (laser) pulses show a rich variety of non-equilibrium effects. For instance, the measurement of spin inertia is a novel tool for accessing long-time spin dynamics in such systems. An external magnetic field is applied in Faraday geometry ($\vec{B}$ parallel to direction of laser beam) while resident charge carriers in the quantum dots are excited by trains of circularly polarized laser pulses with modulated helicity. We extend the current theory of spin inertia from weak pump pulses to strong pulses and observe a number of novel effects, e.g., spin mode locking in Faraday geometry. In another type of pump-probe experiment on quantum dots where the external magnetic field is applied in Voigt geometry ($\vec{B}$ perpendicular to direction of laser beam), the nuclear bath state can be indirectly manipulated via the hyperfine interactions with the periodically pumped resident charge carrier by very long trains of laser pulses. This leads to nuclei-induced frequency focusing (NIFF) of the resident charge carrier spin because the polarizations of the nuclear spins comply with special resonance conditions so that their macroscopic sum (Overhauser field) displays an almost discrete spectrum. We perform comprehensive simulations of this kind of pump-probe experiment to gain a detailed understanding of NIFF. Its application can be used to prolong the coherence time of ensembles of quantum dots significantly.

### Magnetism of the N = 42 kagome lattice antiferromagnet

Schnack, Jürgen

For the paradigmatic frustrated spin-half Heisenberg antiferromagnet on the kagome lattice we performed large-scale numerical investigations of thermodynamic functions by means of the finite-temperature Lanczos method for system sizes of up to N = 42. We present the dependence of magnetization as well as specific heat on temperature and external field and show in particular that a finite-size scaling of specific heat supports the appearance of a low-temperature shoulder below the major maximum. This seems to be the result of a counterintuitive motion of the density of singlet states towards higher energies. Other interesting features that we discuss are the asymmetric melting of the 1/3 magnetization plateau as well the field dependence of the specific heat that exhibits characteristic features caused by the existence of a flat one-magnon band. By comparison with the unfrustrated square-lattice antiferromagnet the tremendous role of frustration in a wide temperature range is illustrated.

### Studying topological spin liquids with tensor networks

Schuch, Norbert

Topological spin liquids are elusive phases of matter, where a system with magnetic interactions does not order magnetically due to strong frustration, but instead orders topologically, i.e. in its local entanglement. This contrast between local symmetries and global entanglement makes these systems notoriously hard to study. In my talk, I will discuss how tensor networks can be used to study topological spin liquids. Tensor networks form a language for the description of complex entangled systems which allows to reconcile local symmetries and global entanglement. I will discuss how this framework allows to understand the topological order through local symmetries in its description, and how this allows to characterize the interplay of local physical symmetries of the system with the topological order. I will also show that tensor networks form a powerful framework for their numerical characterization, allowing to certify the complete absence of magnetic ordering as well as the presence and nature of the topological order, and provide us with powerful tools to directly probe the behavior of the different exotic excitations (anyons) in the system, and they way in which they drive phase transitions.

### Non-local emergent hydrodynamics in a long range interacting spin system

Schuckert, Alexander

Short-range interacting quantum systems with a conserved quantity show universal diffusive behaviour at late times in the absence of quasiparticle excitations. We show how this universality is replaced by a more general transport process in the presence of long-range interactions decaying algebraically, as $r^{-\alpha}$, with distance $r$. While diffusion is recovered for large exponents $\alpha>1.5$, longer-ranged interactions with $0.5<\alpha<1.5$ give rise to effective classical L\'evy flights, a random walk with step sizes following a heavy-tailed distribution. We demonstrate this phenomenon in a long-range interacting XY spin chain, conserving the total magnetization $S_z$, at infinite temperature by employing non-equilibrium quantum field theory and semi-classical phase-space simulations. We find that the space-time dependent spin density profiles show a self-similar behaviour, with a scaling function smoothly covering all stable symmetric distributions as a function of $\alpha$ for $0.5<\alpha<1.5$. In particular, the spin autocorrelation function decays algebraically, with the exponent given by $1/(2\alpha-1)$. Our findings can be readily verified with current trapped ion experiments and may also be observable in critical itinerant ferromagnets.

### Long-lived circulating currents in strongly correlated nanorings

Schuricht, Dirk

We study the time evolving currents flowing in an interacting, ring-shaped nanostructure after a bias voltage has been switched on. The source-to-drain current exhibits the expected relaxation towards its quasi-static equilibrium value at a rate $\Gamma_0$ reflecting the lead-induced broadening of the ring states. In contrast, the current circulating within the ring decays with a different rate $\Gamma$, which is a rapidly decaying function of the interaction strength and thus can take values orders of magnitude below $\Gamma_0$. This implies the existence of a regime in which the nanostructure is far from equilibrium even though the transmitted current is already stationary. We discuss experimental setups to observe the long-lived ring transients.

### Second sound and superfluidity in ultracold quantum gases

Singh, Vijay Pal

Ultracold atom systems are well-controlled and tunable quantum systems, and thereby enable us to explore quantum many-body effects, such as superfluidity, or second sound. In this talk, I will examine second sound and superfluidity in ultracold quantum gases using analytical and simulation techniques. I will report on the second sound measurements in the BEC-BCS crossover and provide a theoretical description of the second sound velocity on the BEC side of the system [1]. Here, I will demonstrate that the second sound velocity vanishes at the superfluid-thermal boundary, which is a defining feature of second sound. In the second part of this talk, I will investigate superfluidity of ultracold quantum gases via laser stirring. I will present the stirring experiments in the BEC-BCS crossover and provide a quantitative analysis of the breakdown of superfluidity [2]. I will then investigate superfluidity of 2D Bose gases across the Kosterlitz-Thouless transition and provide a quantitative understanding of the experiments performed in the Dalibard group [3]. I will also present the noise correlations of 2D Bose gases in short time of flight and use them to determine the phase coherence of the recent experiments at Hamburg [4]. [1] D. Hoffmann, V. P. Singh, T. Paintner, W. Limmer, L. Mathey, and J. H. Denschlag, `Second sound in the BEC-BCS crossover'', forthcoming. [2] W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, and H. Moritz, Phys. Rev. Lett. 114, 095301 (2015); V. P. Singh et al., Phys. Rev. A 93, 023634 (2016). [3] V. P. Singh, C. Weitenberg, J. Dalibard, and L. Mathey, Phys. Rev. A 95, 043631 (2017). [4] V. P. Singh and L. Mathey, Phys. Rev. A 89, 053612 (2014).

### The spin Drude weight of the XXZ chain and generalized hydrodynamics

Sirker, Jesko

Based on a generalized free energy we derive exact thermodynamic Bethe ansatz formulas for the expectation value of the spin current, the spin current-charge, charge-charge correlators, and consequently the Drude weight. These formulas agree with recent conjectures within the generalized hydrodynamics formalism. They follow, however, directly from a proper treatment of the operator expression of the spin current. The result for the Drude weight is identical to the one obtained 20 years ago based on the Kohn formula and TBA. We numerically evaluate the Drude weight for anisotropies Δ=cos(γ) with γ=nπ/m, n≤m integer and coprime. We prove, furthermore, that the high-temperature asymptotics for general γ=πn/m---obtained by analysis of the quantum transfer matrix eigenvalues---agrees with the bound which has been obtained by the construction of quasi-local charges.

### Thermalization and eigenstate thermalization hypothesis in the Holstein polaron model

Stolpp, Jan

The 1d Holstein model is a paradigmatic system to study polaron physics and the nonequilibrium dynamics of charge carriers coupled to phonons. While the electronic relaxation dynamics of a single charge carrier is a much studied topic (see, e.g. [1]), here, we systematically investigate whether the 1d Holstein model in the single-polaron limit is ergodic by checking the criteria of the eigenstate thermalization hypothesis and by testing for established quantum chaos indicators. Using exact diagonalization techniques we find that the level spacing distribution is Wigner-Dyson, which is characteristic for a quantum chaotic system. Remarkably, both the diagonal and offdiagonal matrix elements of typical observables obey properties predicted by the eigenstate thermalization hypothesis. Thus, we found an example in which the coupling term between the electronic and phononic subspaces leads to ergodic behavior, even though the phonon system itself consists of uncoupled, local harmonic oscillators. [1] Phys. Rev. B 91, 104302 (2015)

### On multipartite entanglement and multipartite correlations

Szalay, Szilárd

We briefly review the partial separability based classification of mixed states of multipartite quantum systems of arbitrary number of subsystems. We show how this structure simplifies in the case when not entanglement but correlation is considered. As special cases, we consider the notions of $k$-separability and $k$-producibility (as well as their correlational versions), reveal how these are dual to each other. This can be seen from a much wider perspective, when we consider the entanglement and correlational properties which are invariant under the permutations of the subsystems. This general treatment reveals a new property, which we call $k$-stretchability of entanglement, having advantages over $k$-partitionability and $k$-producibility. We also give the corresponding multipartite correlation and entanglement monotones, being the natural generalizations of mutual information, entanglement entropy and entanglement of formation or relative entropy of entanglement, showing the same lattice structure as the classification (multipartite monotonicity). As illustration, we show some examples coming from molecular-physics. The contribution is based on the works [PhysRevA 92, 042329 (2015)], [SciRep 7, 2237 (2017)] and [JPhysA 51, 485302 (2018)], and on results unpublished yet. (If oral presentation is not possible, I am also happy to present a poster with the same abstract.)

### High-harmonic generation in quantum magnets

Takayoshi, Shintaro

Strong Light-matter interaction results in various intriguing phenomena. A technologically relevant example is the high-harmonic generation (HHG) in quantum systems, which is the basis of atto-second science. HHG originates from the highly nonlinear dynamics of electrons driven by strong laser fields. The phenomenon has been studied for decades in atomic and molecular gases. Recent observations of HHG in semiconductors and liquids have stimulated the condensed matter community to explore and understand HHG in solids. In this work, we propose the new possibility of HHG in quantum spin systems driven by time-dependent magnetic fields, and reveal its mechanism. In contrast to the conventional HHG in electron systems driven by electric fields, the HHG from spin systems reflects the dynamics of magnetic excitations, and thus it can be used to obtain information on the magnetic excitation spectrum as well as it may provide a new laser source in the THz regime. Specifically, we consider the two types of ferromagnetic spin chain models, the Ising model with static longitudinal field and the XXZ model, and we discuss how the existence of external field and quantum fluctuation affects the HHG spectra. Our results demonstrate that the HHG radiation spectra can capture the property of elementary excitations, magnons, in these systems.

### Pumped correlated systems: Spectral properties and long-time limits

Uhrig, Götz

In this talk, two conceptual issues of non-equilibrium physics are addressed and their practical relevance is illustated. First, it is proven that the suitably averaged imaginary part of the two-times Green function can indeed be interpreted as a density of states in fermionic systems. Additionally, we consider how long a pulsing regime has to be in order that Floquet behavior occurs and can be measured. In the second focus we consider how the long-time limit of periodically driven systems including dissipation can be found. This concept is illustrated for periodically laser pumped electronic spins in semiconductor quantum dots. The results compare well with recent experiments. These findings suggest that tailored non-equilibrium states can be prepared by periodic pumping in combination with dissipative processes.

### Coulomb engineering of two-dimensional Mott insulators

van Loon, Erik

Substrates provide a convenient tool for manipulating two-dimensional materials. One way the substrate affects the material is via the screening of the Coulomb interaction. Previous theoretical and experimental works have shown how this kind of Coulomb engineering can be used to control semiconductors. Correlated systems provide an even more fertile ground for Coulomb engineering, since the Coulomb interaction controls the strenth of correlations. Here, we investigate the impact of this substrate screening on two-dimensional Mott insulators. This requires a theoretical description of the interplay of internal and external screening and correlation. We address the metal-insulator transition in the presence of substrate screening and how the size of the gap is altered.

### Are typical Hamiltonian eigenstates similar to random states?

Vidmar, Lev

Studies of nonequilibrium dynamics and thermalization of isolated quantum systems have revealed a crucial role played by Hamiltonian eigenstates when establishing a link between quantum dynamics and quantum statistical physics. In my talk, I will shed some new light on the structure of Hamiltonian eigenstates far above the ground state from the perspective of bipartite von Neumann entanglement entropy. First I will focus on eigenstates of generic many-body Hamiltonians (also denoted as 'quantum chaotic Hamiltonians') with particle number conservation [1]. I will study eigenstates of quantum spin chains in nonintegrable regime, as well as random pure states. The main question I am going to address is how different are typical eigenstates of physical Hamiltonians from typical states in the Hilbert space. In the second part, I will focus on quadratic fermionic Hamiltonians [2], with a particular emphasis on the paradigmatic quantum Ising model in one dimension [3,4]. In this class of Hamiltonians, typical eigenstates are much less entangled than typical states in the Hilbert space. I will argue that the leading term of the average (over all eigenstates) entanglement entropy exhibits a volume-law scaling that is universal for translationally invariant quadratic models. The subleading term is constant at the critical field for the quantum phase transition and vanishes otherwise (in the thermodynamic limit), i.e., the critical field can be identified from subleading corrections to the average entanglement entropy. [1] Vidmar and Rigol, Phys. Rev. Lett. 119, 220603 (2017) [2] Vidmar, Hackl, Bianchi and Rigol, Phys. Rev. Lett. 119, 020601 (2017) [3] Vidmar, Hackl, Bianchi and Rigol, Phys. Rev. Lett. 121, 220602 (2018) [4] Hackl, Vidmar, Rigol and Bianchi, in preparation

### Approximately Quantized Thermal Hall Effect of Chiral Liquids Coupled to Phonons

Vinkler-Aviv, Yuval

The recent observation of a half-integer quantized thermal Hall effect in α−RuCl3 is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity $\kappa_xy$ is never exactly quantized in real materials. In this talk I will examine how phonons affect the quantization of the thermal conductivity, focusing on the edge theory. As an example, I consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized, and in fact I argue that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. For sufficiently clean systems the leading correction to the quantized thermal Hall effect, $\Delta\kappa_xy/T∼sign(B)T^2$, arises from an intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.

### Uncovering non-Fermi-liquid behavior in Hund metals

von Delft, Jan

Hund metals are multi-orbital materials with broad bands which are correlated via the ferromagnetic Hund coupling $J$, rather than the Hubbard interaction $U$. $J$ implements Hund's rule, favoring electronic states with maximal spin. Examples include transition metal oxides with partially filled d-shells, such as ruthenates, or iron-based superconductors. In Hund metals the interplay between spin and orbital degrees of freedom can lead to spin-orbital separation (SOS), meaning that the energy scales below which spin and orbital degrees are screened differ, $T_{\rm spin} < T_{\rm orb}$. The low-energy regime below $T_{\rm spin}$ shows Fermi-liquid behavior. The intermediate energy window, $[T_{\rm spin}, T_{\rm orb}$, by contrast, shows incoherent behavior, featuring almost fully screened orbital degrees of freedom coupled to almost free spin degrees of freedom. Experimentally, the incoherent regime shows bad-metal behavior, hence it is of great interest to understand it theoretically. It has been conjectured to have non-Fermi-liquid (NFL) properties, but the nature of the putative underlying NFL state has not yet been clarified. We have studied its properties within the context of a minimal 3-orbital Hubbard-Hund model for a Hund metal. Treating this model using dynamical mean field leads to a self-consistent Anderson impurity model in which bath and impurity both have spin and orbital degrees of freedom. We have studied the Kondo version of this impurity model, which can be tuned such that the NFL energy window is very wide. This allows us to unambiguously identify the NFL fixed point governing this intermediate-energy regime. In this regime the dynamical spin and orbital susceptibilities show anomalous NFL power law behavior. We compute the power law exponents using both conformal field theory and the numerical renormalization group, finding excellent agreement between both methods.

Wessel, Stefan