Korrelationstage 2019

We propose a lattice model for quantum multi wires on a three dimensional substrate and map them onto effective two-dimensional lattices using the Block-Lanczos algorithm. This mapping is a generalization of the mapping introduced in [1,2] and [3] for single-wire systems. Then, we approximate the resulting two-dimensional lattice by taking only a limited number of legs to form a narrow ladder model (NLM). We investigate the validity of this approximation and discuss the influence of the wire-substrate hybridization on the wire-wire coupling using noninteracting two-wire systems. Moreover, we use the density matrix renormalization (DMRG) group to investigate correlated NLM consisting of spinless-fermion wires. We us DMRG to study the mutual influence of wire-wire and wire-substrate couplings on quasi-one-dimensional phases such as Luttinger liquid and charge density wave. Support from the DFG through the Research Units FOR 1700 is gratefully acknowledged. [1] A. Abdelwahab, E. Jeckelmann, and M. Hohenadler, Phys. Rev. B 96, 035445 (2017). [2] A. Abdelwahab, E. Jeckelmann, and M. Hohenadler, Phys. Rev. B 96, 035446 (2017). [3] Anas Abdelwahab and Eric Jeckelmann, Luttinger liquid and charge-density-wave phases in a spinless fermion wire on a semiconducting substrate, Phys. Rev. B 98, 235138 (2018)

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.

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 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.

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 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.

Motivated by recent progress in applying techniques from the field of artificial neural networks (ANNs) to quantum many-body physics, we investigate as to what extent the flexibility of ANNs can be used to efficiently study systems that host chiral topological phases such as fractional quantum Hall (FQH) phases. With benchmark examples, we demonstrate that training ANNs of restricted Boltzmann machine type in the framework of variational Monte Carlo can numerically solve FQH problems to good approximation. Furthermore, we show by explicit construction how n-body correlations can be kept at an exact level with ANN wave-functions exhibiting polynomial scaling with power n in system size. Using this construction, we analytically represent the paradigmatic Laughlin wave-function as an ANN state.

Quantum entanglement may have various origins ranging from solely interaction-driven quantum correlations to single-particle effects. Here, we explore the dependence of entanglement on time-dependent single-particle basis transformations in fermionic quantum many-body systems, thus aiming at isolating single-particle sources of entanglement growth in quench dynamics. Using exact diagonalization methods, for paradigmatic non-integrable models we compare to the standard real space cut various physically motivated bipartitions. Moreover, we search for a minimal entanglement basis using local optimization algorithms, which at short to intermediate post-quench times yields a significant reduction of entanglement beyond a dynamical Hartree-Fock solution. In the long-time limit, we identify an asymptotic universality of entanglement for weakly interacting systems, as well as a cross-over from dominant real-space to momentum-space entanglement in Hubbard-models undergoing an interaction quench. Finally, we discuss the relevance of our findings for the development of tensor network based algorithms for quantum dynamics.

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).

We study the dynamics of one and two dimensional disordered lattice bosons/ fermions initialised to a Fock state with a pattern of 1 and 0 particles on A and $\bar{A}$ sites respectively. For non-interacting systems we establish a universal relation between the long time density imbalance between A and $\bar{A}$ sites, I(∞), the localization length ξ$_l$ , and the geometry of the initial pattern. For alternating initial pattern of 1 and 0 particles in 1 dimension, I(∞) = tanh[a /ξ$_l$] , where a is the lattice spacing. For systems with mobility edge, we find analytic relations between I(∞), the effective localization length $\tilde{ξ}_l$ and the fraction of localised states $f_l$. The imbalance as a function of disorder shows non-analytic behaviour when the mobility edge passes through a band edge. For interacting bosonic systems, we show that dissipative processes lead to a decay of the memory of initial conditions. However, the excitations created in the process act as a bath, whose noise correlators retain information of the initial pattern. This sustains a finite imbalance at long times in strongly disordered interacting systems. Ref: arXiv:1906.02205 (2019) [Under review process of Physical Review Letters] 


Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we find further evidence for anomalous thermalization in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in $S\frac{z}{i}S\frac{z}{i+r}$ correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A quantitative quasi-degenerate perturbation theory calculation of these correlators yields a surprising agreement of the full distribution with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the $S\frac{z}{i}S\frac{z}{i+r}$ correlator exhibits striking differences between the MBL and Anderson insulator cases.

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

We consider the one-dimensional Hubbard model with periodically modulated repulsive interactions, which is equivalent to two species of hard-core bosons in a one-dimensional optical lattice. Using Floquet theory the periodic model can be mapped to an effective Hamiltonian for high frequencies, which is described by a static interaction and hopping parameters that depend on the local densities. We establish the full quantum phase diagram for half-integer filling for this system. Surprisingly, the density-dependent reduction of hopping drives a quantum phase transition into a superfluid phase. For negative hopping a previously unknown state is found, where one species induces a gauge phase of the other species, which leads to a superfluid phase of gauge-dressed particles.

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).

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.

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.

We demonstrate the manifestation of structures underlying the Hawking-Unurh effect of spacetime horizons(black holes) in the dynamics of potentials and shears applied on quantum Hall systems. The central object underlying the phenomena of thermality associated with space-time horizons is the ‘Rindler Hamiltonian’, which is a specific instance of an entanglement Hamiltonian. This object is nothing but a boost generator in Minkowski spacetime, which in turn generates time translation (as a Hamiltonian) in a wedge-shaped region restricted by a lightcone/horizon. The same object leads to Bogoliubov-type transformations on the operators acting on the quantum mechanical vacuum, thus leading to thermality of a state restricted to the wedge. Using a very important isomorphism between the Lie-algebras of Lorentz group(so(2,1)) of Minkowski spacetime and that of area-preserving transformations(sl(2,R)) on LLLs, we establish an exact parallel of the Rindler Hamiltonian in terms of saddle potential/ shears/ squeeze operators in the LLL. Through this, the Rindler Hamiltonian dynamics is shown to be captured through an inverted Harmonic oscillator potential, an archetypal model as ubiquitous in physics as the simple Harmonic oscillator. The scattering poles of this potential are associated with Riemann zeroes of Berry-Keating Hamiltonian. Further ramifications of this analysis lead us to the study of quasi-normal modes, time-decay of wave-packet dynamics in quantum point contact geometries and manifestation of Wigner rotation in Hall viscosity. Connections to certain fundamental theorem of Bisognano-Wichmann and half-space quantum mechanics are suggested. *Partially done in collaboration with Varsha Subramanyan, Barry Bradlyn and Smitha Vishveshwara (UIUC).

In this talk I will show how lattice gauge theories can display many-body localization dynamics in the absence of disorder as a consequence of local constraints induced by gauge invariance. The starting point is the observation that, for some generic homogeneous initial conditions, the time-evolved state can be decomposed into different superselection sectors as a consequence of Gauss law in such a way that it realizes an effective disorder average. By carrying out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions, it is shown that the dynamics can become nonergodic leading to a slow, double-logarithmic entanglement growth. Further, it will be shown how the nonergodic behavior induced by this localization mechanism can give rise to eigenstate phases in homogeneous systems. Specifically, I will introduce a model for a 'gauge time crystal' breaking spatiotemporal symmetries.

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.

The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the $e_g$ Mott insulator $Ba_3CuSb_2O_9$ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions. https://arxiv.org/abs/1908.09224

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.

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.

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.

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 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.

Four-point correlation functions (two-particle Green's functions) commonly appear in various contexts of the theory of strongly correlated systems. For example, four-point functions describe the nonlocal response of the system in experiments, such as neutron scattering and resonant inelastic X-ray scattering. They are also key ingredients in extending dynamical mean-field theory (DMFT) to incorporate nonlocal correlations. In both contexts, to compare with experimental observation, it is necessary to compute four-point functions on the real-frequency axes at low temperatures. Here we develop the numerical renormalization group (NRG) method for computing four-point correlation functions in quantum impurity systems. First, we derive the Lehmann representation for general four-point functions (i) in imaginary Matsubara frequencies, (ii) on the real-frequency axes at zero temperature, and (iii) on the Keldysh contour. By using a complete basis of many-body energy eigenstates constructed within NRG, four-point functions can be computed at arbitrarily low temperatures. We present results for paradigmatic models, including the effective quantum impurity model arising in DMFT treatments of the Hubbard model.

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 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).

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.

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.

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.

Locality imposes stringent constraints on the spreading of information in nonrelativistic quantum systems, which is reminiscent of a "light-cone," a casual structure arising in their relativistic counterparts. Long-range interactions can potentially soften such constraints, allowing almost instantaneous long jumps of particles, thus defying causality. Since interactions decaying as a power-law with distance, $r^{-\alpha}$, are ubiquitous in nature, it is pertinent to understand what is the fate of causality and information spreading in such systems. Using a numerically exact technique we address these questions by studying the out-of-time-order correlation function of a representative generic system in one-dimension. We show that while the interactions are long-range, their effect on information spreading is asymptotically negligible as long as $\alpha>1$. In this range we find a complex compound behavior, where after a short transient a fully local behavior emerges, yielding asymptotic "light-cones" virtually indistinguishable from "light-cones" in corresponding local models. The long-range nature of the interaction is only expressed in the power-law leaking of information from the "light-cone," with the same exponent as the exponent of the interaction, $\alpha$. Our results directly imply that all previously obtained rigorous bounds on information spreading in long-range interacting systems are not tight, and thus could be improved. Reference: Phys. Rev. A 99, 010105(R) [https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.010105]

Phases and phase transitions provide an important framework to understand the physics of strongly correlated quantum many-body systems. Topologically ordered phases of matter are particularly challenging in this context, because they are characterized by long-range entanglement and go beyond the Landau-Ginzburg theory. A few tools have been developed to study topological phase transitions, but the needed computations are generally demanding, they typically require the system to have particular boundary conditions, and they often provide only partial information. There is hence a high demand for developing further probes. Here, we propose to use the study of quasiparticle properties to detect phase transitions. Topologically ordered states support anyonic quasiparticles with special braiding properties and fractional charge. Being able to generate a given type of anyons in a system is a direct method to detect the topology, and the approach is independent from the choice of boundary conditions. We provide three examples, and for all of them we find that it is sufficient to study the anyon charge to detect the phase transition point. This makes the method numerically cheap. Ref.- arXiv:1909.02046.

The non-linear Hall effect is allowed by time-reversal symmetry and is controlled by the "Berry curvature dipole”. In this work, we elucidate on deeper underpinnings of the Berry curvature dipole. We show that the Berry curvature dipole plays the role of a non-linear version of the Drude weight and offers an “order parameter” for broken inversion in metals. We derive a “quantum rectification sum rule” in time-reversal invariant materials in which the frequency integrated rectification conductivity depends purely on the quantum geometry of the ground state wave-function and whose intra-band spectral weight is completely exhausted by the Berry curvature dipole term.

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.

Charge transport measurements in high magnetic fields recently shed new light on the non-superconducting ground state in cuprate high-$T_c$ superconductors [1]. In particular, Hall measurements yield a drop of the Hall number indicating a phase transition associated with a Fermi surface reconstruction. On the theoretical side, spiral magnetic order (or quasi-order) remains a hot candidate for the Fermi surface reconstruction mechanism. \\ \\ The electromagnetic response of spiral magnetic states has already been analyzed by Voruganti et al. for small relaxation rates [2]. However, the relaxation rate in the cuprate samples studied experimentally is sizable. We have, thus, derived, for the first time, a complete formula (including all interband contributions) for the Hall conductivity in the low field limit $\omega_c\tau\ll 1$ [3]. \\ \\ We use the complete expressions to study the importance of a sizable relaxation rate and show that the observed Hall number drop in cuprates can be fitted with realistic parameters. \\ \\ [1] Badoux et al., Nature 531, 210 (2016) [2] Voruganti et al., Phys. Rev. B 45, 13945 (1992) [3] Mitscherling and Metzner, Phys Rev. B 98, 195126 (2018)

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.

Periodic driving in many-body systems offer a new route to realize novel transient states via Floquet engineering [1,2] or strong optical excitation [3]. Here, we investigate an optically excited one-dimensional ionic Hubbard model with an exact time-dependent Schrödinger equation solver. We characterize the driven system by transient conductivity and time-resolved spectral functions in addition to other local observables. We find that these quantities do not necessarily correspond to each other as in the equilibrium situations. For instance, the Drude peak oscillates at the pump frequency and its second harmonic, while the doublon density oscillates only at the second harmonic. Furthermore, two different definitions of transient conductivity give slightly different results. [1] Rev. Mod. Phys. 89 011004 (2017), [2] Annu. Rev. Condens. Matter Phys. 10, 387 (2019), [3] Phil. Trans. R. Soc. A 20170478, 377 (2019)

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.

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)

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.

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)

We investigate the out-of-equilibrium properties of a system of interacting bosons on a lattice. We present a Floquet driving scheme that induces the motion of the particles with direct link to a model of fully connected clock variables with n-arms (n ≥ 2). The clock-like motion of the particles is at the core of a time crystalline phase undergoing period-n-tupling. Tilting the lattice with an on-site potential, we show the emergence of a second characteristic timescale on top of the period-n-tupling. Such a new timescale depends on the microscopic parameters and is incommensurate with the Floquet period, signaling a dynamical phase that we coin discrete quasi time crystal. We study the complete dynamical phase diagram featuring also thermal and oscillatory phases. Our simple, yet very rich model can be realized with ultracold atoms in optical lattices.

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.

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.

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.

Geometric and gauge constraints can lead to perfectly flat single-particle dispersion relation in a lattice, in particular through so-called Aharonov-Bohm caging. Once interactions are turned on, a wealth of interesting phenomena can arise. Here we examine two of them in one-dimensional (1D) systems, namely [1] fractional topological phases and [2] exotic transport properties: [1] We show that a hierarchy of symmetry-protected topological (SPT) phases at filling $1/(r+2)$ can emerge for fermions in presence of interactions within the first $r$ neighbouring sites, once the single-particle band structure describes a (crystalline) topological insulator. In sharp contrast to the non-interacting limit, however, these topological density waves do not follow the boundary-edge correspondence, as their edge modes are gapped. [2] We explore the bosonic phase diagram of a chain of rhombi subject to a magnetic flux and local repulsion: Besides the more conventional Mott-insulator and superfluid (Luttinger liquid) phases, a pair-superfluid (pair-Luttinger liquid) phase emerges there. We find however that such exotic phase is very sensitive to changes away from perfect frustration (half-flux), and provide some suggestions to make it more resilient. We also study the bipartite entanglement properties of the chain: While having the same central charge, the two gapless phases display a fundamental difference in the properties of the low-lying entanglement spectrum levels. [1] S. Barbarino, D. Rossini, M. Rizzi, R. Fazio, G.E. Santoro, and M. Dalmonte, New J Phys. 21, 043048 (2019) [2] C. Cartwright, G. De Chiara, and M. Rizzi, Phys. Rev. B 98, 184508 (2018)

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.

In crystalline structures, geometrical frustration is mainly observed in triangular structures. Anti-ferromagnetic couplings induce very complex ground state structures which are highly degenerate. The tetrahedral structure of the pyrochlore lattice yields a frustrated system. One of the most powerful tools for investigating thermodynamic properties are quantum Monte Carlo techniques. However, applying Monte Carlo methods to frustrated systems fail due to the sign problem. To overcome this issue, we investigate many-body systems using quantum typicality. This approach yields insights into frustrated lattices far beyond exact diagonalization. To approximate the thermodynamic limit, we expand the pyrochlore lattice starting from a single unit cell and systematically add other unit cells. Each expansion contributes to the approximation of the thermodynamic limit. Employing a unit cell expansion rather than a site-by-site expansion, we are able to treat a small number of large frustrated clusters, which can then be solved by typicality. Using these techniques, we obtain insights into how different cluster sizes influence the thermodynamic limit and we investigate the differences between the classical and quantum (s=1/2,1) model.

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.

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.

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.

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).

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.

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)

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), and 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, being sensitive in a balanced way to both the maximal size of correlated (or entangled) subsystems and the minimal number of subsystems uncorrelated (or separable) from one another. 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)], [JPhysA 51, 485302 (2018)], and [arXiv:1906.10798 [quant-ph]].

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.

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.

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.

Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. In this work we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e. power-law) solutions, corresponding to the metastable insulator at the boundary of metal-insulator coexistence region, which can be linked to the physics of the pseudogap Anderson model. While our state-of-the-art numerical renormalization group calculations reveal that this asymptotic regime is restricted to very small energies and temperatures, we uncover the existence of a wide crossover regime where the single-particle spectrum displays a different power law. We show that it is this power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point.

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.

We present numerical evidence for the emergence of an extended valence bond solid (VBS) phase at T=0 in the kagome S=1/2 Heisenberg antiferromagnet with ferromagnetic further-neighbor interactions. The VBS is located at the boundary between two magnetically ordered regions and extends close to the nearest-neighbor Heisenberg point. It exhibits a diamond-like singlet covering pattern with a 12-site unit-cell. Our results suggest the possibility of a direct, possibly continuous, quantum phase transition from the neighboring q=0 coplanar magnetically ordered phase into the VBS phase. Moreover, a second phase which breaks lattice symmetries, and is of likely spin-nematic type, is found close to the transition to the ferromagnetic phase. The results have been obtained using numerical Exact Diagonalization. We discuss implications of our results on the nature of nearest-neighbor Heisenberg antiferromagnet.