Ergodicity Breaking and Anomalous Transport in Quantum Many-Body Systems

Many-Body Localized (MBL) phases are customarily characterized with global entanglement measures, like the entanglement entropy. In this poster, I will present recent results regarding local properties of entanglement, therefore characterizing its spreading after a quench in a more detailed way. I will focus, in particular, on the space-time structure of the relaxation times of the concurrence, a two-qubit entanglement monotone. I will show how such times are spatially correlated, giving rise to a quantum, dynamical correlation length. Finally, I will highlight the similarities with the phenomenon of "dynamical heterogeneities" that takes place in classical glasses, providing a yet unrecognized connection between the behavior of classical glasses and the genuine quantum dynamics of MBL systems.

Topological phases of matter are the center of much current interest. Traditionally such states are prepared by tuning the system’s Hamiltonian while coupling it to a generic low-temperature bath. However, this approach is often ineffective, especially in cold-atom systems. We have recently shown that topological phases can emerge much more efficiently even in the absence of a Hamiltonian, by properly engineering the interaction of the system with its environment, to directly drive the system into the desired state. Disorder is inherent in any experimental implementation. How does it affect this behavior? Generalizing appropriate topological indexes (e.g., Chern number) to the dissipative case, we find that the topological phases are robust to weak disorder. Strong disorder can cause transition to localization. Surprisingly, while disorder in the dissipative dynamics leads to the same universality class as in equilibrium, we find evidence that disorder in the Hamiltonian part gives rise to a new critical exponent. This new universality class could be tested in cold atom experiments.

TBA

The Rosenzweig-Porter random matrix ensemble is analytically tractable and covers both an ergodic, delocalized yet nonergodic, and localized phase. A seminal work by Kravtsov and co-authors [1] argues that this ensemble can serve as a qualitative phenomenological model for the level statistics and fractality of eigenstates as observed across the many-body localization transition. Motivated by the observation of many-body localization in periodically driven (Floquet) systems [2], we propose a unitary analogue of the Rosenzweig-Porter ensemble. We define this ensemble as the outcome of a Dyson Brownian motion process [3]. We numerically validate some key properties for both the eigenvalues and the eigenvectors. [1] V. E. Kravtsov, I. M. Khaymovich, E. Cuevas, and M. Amini, New J. Phys. 17, 122002 (2015). [2] P. Ponte, Z. Papić, F. Huveneers, and D. A. Abanin, Phys. Rev. Lett. 114, 140401 (2015). [3] F. J. Dyson, J. Math. Phys. 3, 1196 (1962).

We combine quantum renormalization group approaches with deep artificial neural networks for the description of the real-time evolution in strongly disordered quantum matter. We find that this allows us to accurately compute the long-time coherent dynamics of large many-body localized systems in nonperturbative regimes including the effects of many-body resonances. Concretely, we use this approach to describe the spatiotemporal buildup of many-body localized spin-glass order in random Ising chains. We observe a fundamental difference to a noninteracting Anderson insulating Ising chain, where the order only develops over a finite spatial range. We further apply the approach to interacting Rydberg systems, highlighting that our method can be used also for the description of the real-time dynamics of nonergodic quantum matter in a general context.

We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some "landmarks" within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i).

Quantum coherence quantifies the amount of superposition a quantum state can have in a given basis. Since there is a difference in the structure of eigenstates of the ergodic and many-body localized systems, we expect them also to differ in terms of their coherences in a given basis. Here, we numerically calculate different measures of quantum coherence in the excited eigenstates of an interacting disordered Hamiltonian as a function of the disorder. We show that quantum coherence can be used as an order parameter to detect the well-studied ergodic to many-body-localized phase transition. We also perform quantum quench studies to distinguish the behavior of coherence in thermalized and localized phases. We then present a protocol to calculate measurement-based localizable coherence to investigate the thermal and many-body localized phases. The protocol allows one to investigate quantum correlations experimentally in a non-destructive way, in contrast to measures that require tracing out a subsystem, which always destroys coherence and correlation.

Strong electron-electron interactions are challenging to capture theoretically. A rare example of an analytically tractable model is theSachdev-Ye-Kitaev (SYK) model, which owes its tractability to thestructureless and therefore artificial design: interactions are restricted to two body terms, whose matrix elements are randomly chosen andtherefore do not commute with the local density, a fundamental symmetry of realistic electron-electron interactions. We here investigate a derivative of the SYK model, restoring this fundamental symmetry [1]. It features density-density-type interactions as well as a randomized single body term. We present numerical evidence that this mode lhas a rich phase structure, featuring two integrable phases separatedby several intermediate phases, including a chaotic one. The latter exhibits several key characterstics of the SYK model including the spectral and wave function statistics and therefore should be adiabatically connected to the non-Fermi liquid phase of the original SYK model.Thus, the presented model provides a further element for bridging theSYK-model and microscopic realism. [1] J. Dieplinger, S. Bera, F. Evers, Annals of Physics, 168503 (2021)

We study the transport properties of generic out-of-equilibrium quantum systems connected to fermionic reservoirs. We develop a new method, based on an expansion of the current in terms of the inverse system size and out of equilibrium formulations such as the Keldysh technique and the Meir-Wingreen formula. Our method allows a simple and compact derivation of the current for a large class of systems showing diffusive/ohmic behavior. In addition, we obtain exact solutions for a large class of quantum stochastic Hamiltonians (QSHs) with time and space dependent noise, using a self consistent Born diagrammatic method in the Keldysh representation. We show that these QSHs exhibit diffusive regimes which are encoded in the Keldysh component of the single particle Green's function. The exact solution for these QSHs models confirms the validity of our system size expansion ansatz, and its efficiency in capturing the transport properties.

We simulate the dynamics of a spin-1/2 chain with nearest neighbor Ising interactions, quenched disorder and periodic driving over 57 qubits on a current quantum computer. Based on the dynamics of local spin depolarisation we observe discrete time crystalline behaviour due to many body localisation. We probe random initial states along with fully polarised states. In order to extract the signal from the noisy data produced by current quantum computer devices, we develop a strategy for error mitigation. A transition between DTC and a thermal phase is observed via critical fluctuations in the sub-harmonic frequency response of the system, as well as a significant speed-up of spin depolarisation.

Typical experiments, designed to detect the many-body delocalization-localization transition, measure the dynamical properties of such systems [1]. However, much work has been done to provide evidence of the transition in the structure of eigenstates. In our recent works [2, 3], we introduce a new quantitative measure for the Fock-space localization [4], computed in the eigenstates. It has a distinct behaviour in the delocalized and localized phase, observed both for bosons [2] and fermions [3], and is potentially useful for the analysis of future experiments. Its scaling properties in the interacting systems are distinct from those in non-interacting systems [3] which points at a different mechanism for the transitions. Moreover, in fermionic systems, we extract a spatial subsystem entropy from the one-particle density matrix (OPDM) and observe that such entropy provides an upper bound on the entanglement entropy [5]. Interestingly, in the MBL regime, the OPDM entropy exhibits the main features of localization, i.e., the area law of eigenstates and the logarithmic growth with time after a quantum quench [5], and it thus provides an additional diagnostic tool for experiments. [1] See, e.g., Lukin et al. Science 364, 256 (2019), Choi et al, Science 352, 1547 (2016) [2] M. Hopjan and F. Heidrich-Meisner, Phys. Rev. A 101, 063617 (2020) [3] M. Hopjan, G. Orso and F. Heidrich-Meisner, arXiv:2105.10584 (2021) [4] S. Bera, H. Schomerus, F. Heidrich-Meisner, and J. H. Bardarson, Phys. Rev. Lett. 115, 046603 (2015) [5] M. Hopjan, F. Heidrich-Meisner and V. Alba, Phys. Rev. B 104, 035129 (2021)

Quantum scars have been known for decades to exist in quantum systems of low dimensionality (e.g. ``quantum billiards''): While most eigenstates of a classically chaotic system are typically spread across the accessible phase space, individual states exist that are concentrated along unstable classical periodic orbits. On the other hand, recent studies in many-body quantum systems that admit no known meaningful classical limits have revealed eigenstates - now termed ``quantum many-body scars'' - that feature quantum mechanical properties reminiscent of scenarios of quantum scarring. An unambiguous classification as scars in the original sense, however, remains controversial, if not fundamentally impossible due to the lack of a classical limit. In order to bridge this gap, we investigate the phenomenon of quantum scarring in the prototypical Bose-Hubbard model, a many-body quantum system that combines both, a well-defined formally classical description in form of mean-field equations and the typical high-dimensionality of many-body systems identified with the number of sites that constitute the one-body state space. Along particular periodic mean-field solutions we find a class of quantum states that we identify as quantum scars in the mean-field regime and which persist in the deep quantum regime of low filling factor.

Spin quantum Hall (SQH) transition is a superconducting counterpart of the quantum Hall transition. In presence of disorder, scaling of wave function moments exhibits multifractality (MF) at the SQH critical point. The MF at the SQH transition was studied in previous works. In particular, it was found numerically that the MF spectrum exhibits clear (but relatively weak) deviations from parabolicity. The concept of MF can be extended to a much broader class of local observables built out of wave functions. To reflect this, we introduce the term "generalized MF". In this work, we perform a detailed analytical and numerical study of the generalized MF at the SQH transition. By using the non-linear sigma model formalism, we determine pure-scaling composite operators that correspond to various representations (that can be labelled by Young tableaus or their extension). Further, we perform a "translation" from the field-theory language to that of wave-function correlators. Using the network model of class C, we verify numerically that these correlators exhibit the generalized MF scaling. Very remarkaby, the numerically determined exponents strongly violate the "generalized parabolicity" (proportionality to the quadratic Casimir invariant). At the same time, the generalized parabolicity can be shown analytically to hold at a 2D localization-transition point if one makes assumptions of the abelian fusion of composite operators and of local conformal invariance of the theory. Since the abelian fusion is verified explicitly, our numerical results point out to a violation of the local conformal invariance at the SQH transition.

The recent advances in the world of cold atoms greatly motivated theoreticians to study strongly correlated systems given the possibility of engineering a plethora of interesting models with unprecedented precision in the lab. A prominent example is the 1d interacting Bose gas, an integrable model, which has been extensively studied in several out-of-equilibrium protocols, among them interaction changes. The Bose gas can be realised with repulsive and attractive interaction strength, where the latter case features bound states of atoms. We investigate the bound-state production by adiabatically changing the interaction from repulsive to attractive. The framework of Generalized Hydrodynamics allows for the description of slow interaction changes within the repulsive or attractive phase. We here present a method to connect the two phases, thereby giving an exact analytical expression for the bound-state production that is valid for arbitrary initial states. Moreover, we take the semi-classical limit of the 1d Bose-gas and specifically this protocol arriving at the Non-Linear Schroedinger equation which is not only in itself of interest but also provides the possibility of rigorous numerical checks.

We analytically study shock wave in the Josephson transmission line (JTL) in the presence of ohmic dissipation. When ohmic resistors shunt the Josephson junctions (JJ) or are introduced in series with the ground capacitors the shock is broadened. When ohmic resistors are in series with the JJ, the shock remains sharp, same as it was in the absence of dissipation. In all the cases considered, ohmic resistors don't influence the shock propagation velocity. We study an alternative to the shock wave - an expansion fan - in the framework of the simple wave approximation for the dissipationless JTL and formulate the generalization of the approximation for the JTL with ohmic dissipation.

Theoretical and experimental studies in the last decade have uncovered an anomalous transport law - super-diffusion - in a diverse array of models. We introduce a new class of classical integrable models on a discrete space-time lattice and show how they arise as natural discretizations of nonrelativistic nonlinear sigma models. The discrete integrability-preserving structure of the dynamics enables efficient numerical simulations. The phenomenon of superdiffusion and Kardar-Parisi-Zhang physics are shown to occur in the entire family of models with non-abelian symmetry and a conjecture of "superuniversality" is formulated. We also introduce a uniaxial deformation of the basic SO(3) model and study the transport coefficients in the easy axis and easy plane regimes.

The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour Heisenberg chain, with temperature as tuning parameter. Our numerics expose strikingly different spin dynamics between the antiferromagnet, where it is largely diffusive, and the ferromagnet, where we observe strong evidence either of spin super-diffusion or an extremely slow crossover to diffusion. This difference also governs the equilibration after a quench, and, remarkably, is apparent even at very high temperatures.

The nonlocal kinetic equation unifies the achievements of the transport in dense quantum gases with the Landau theory of quasiclassical transport in Fermi systems. Large cancellations in the off-shell motion appear which are hidden usually in non-Markovian behaviors [1]. The remaining corrections are expressed in terms of shifts in space and time that characterize the non-locality of the scattering process [2]. In this way quantum transport is possible to recast into a quasi-classical picture [3]. The balance equations for the density, momentum, energy and entropy include besides quasiparticle also the correlated two-particle contributions beyond the Landau theory [4]. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. For Maxwellian particles a sign change of the latent heat is reported at a universal ratio of scattering length to the thermal De Broglie wavelength. This is interpreted as a change from correlational heating to cooling [5]. Compared to the quantum Boltzmann equation, the presented nonlocal form of virial corrections only slightly increases the numerical demands in implementations [6].\newline [1] Ann. Phys. 294 (2001) 135, [2] Phys. Rev. C 59 (1999) 3052, [3] "Interacting Systems far from Equilibrium -Quantum Kinetic Theory", Oxford University Press, (2017), ISBN 9780198797241, [4] Phys. Rev. E 96 (2017) 032106, [5] Phys. Rev. B 97 (2018) 195142, [6] Phys. Rev. Lett. 82 (1999) 3767, Phys. Rev. C 62 (2000) 44606, Phys. Rev. 62 (2000) 64602, Phys. Rev. C 63 (2001) 034619.

We study spinless bosons on 3 and 4 sites with onsite interactions – the Bose-Hubbard model - in the classical limit of large particle number. Ergodicity is broken by increasing or decreasing the interaction strength. For very small or very large interaction strengths the model is solvable, while for intermediate interaction strengths the model is not fully ergodic but highly mixed. In the mixed phase ergodicity measures like eigenvalue and eigenstate statistics as well as finite size scaling of the Eigenstate Thermalization Hypothesis deviate from random matrix predictions and from predictions for integrable systems. The classical limit further allows a comparison between classical and quantum ergodicity measures. These agree remarkably well. The more chaotic the quantum phase space is, the more chaotic is the classical phase space, and vice versa. Further, in the classical phase space regular and chaotic trajectories coexist, highlighting the mixed nature of the model on a few sites. I will present a detailed study of ergodicity measures of the classical and quantum Bose-Hubbard model based on the mentioned publication and new unpublished results.

Taking the Hatano-Nelson model as a concrete example, we first consider how diffusion occurs in a non-Hermitian disordered system, and show that it is very different from the Hermitian case. Interestingly, a cascade like diffusion process of an initial wave packet as in the Hermitian case is suppressed in the clean limit and at weak disorder, while it revives in the vicinity of the localization-delocalization transition. Based on this observation, we then analyze how the entanglement entropy of the system evolves in the interacting non-Hermitian model, revealing its non-monotonic evolution in time. We clarify the different roles of dephasing in the time evolution of entanglement entropy in Hermitian and non-Hermitian systems.

We investigate the stationary state of a quenched XY model. Interestingly, quenches along the critical line display a surprising feature. Even though the stationary state shows a volume-law entanglement and exponential decay of 2-point correlations, the state has hidden quantum correlations in spite of a quench. These correlations are captured by the mutual information and its quantum nature is verified by the upper-bound of log-negativity. Both of them show logarithmic divergence with the subsystem size which are signatures of quantum criticality. Furthermore, the mutual information correlation length diverges. Does it imply a new phase transition occurring entirely in the stationary state? If so, the phases are yet to be characterized.

We study the dynamics of a monitored single particle in an one-dimensional, Anderson-localized system. The time evolution is governed by Hamiltonian dynamics for fixed time intervals, interrupted by local projective measurements. The competition between disorder induced localization and measurement induced jumps leads to interesting behaviour of readout-averaged quantities. We find that measurements at random positions delocalize the average position, similar to a classical random walk. Along each quantum trajectory the particle remains localized, however with a modified localization length. In contrast to measurement induced delocalization, controlled measurements can be used to introduce transport in the system and localize the particle at a chosen site. In this sense, the measurements provide a controlled environment for the particle. Using measurements to control correlations in a many-body system is an abundant topic for future research.

Martin Puschmann$^1$, Daniel Hernangómez-Pérez$^2$, Bruno Lang$^3$, Soumya Bera$^4$, and Ferdinand Evers$^1$ 1) Institute of Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany 2) Department of Molecular Chemistry and Material Science, Weizmann Institute of Science, Rehovot 7610001, Israel 3) IMACM and Institute of Applied Computer Science, Bergische Universität Wuppertal, 42119 Wuppertal, Germany 4) Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India The quantum Hall transitions are still one of the bigger mysteries of condensed matter theory. In the past twenty years several conjectures have been made as to what the field theory of the critical fixed point of the integer (class A) quantum Hall transition could be. [1--8] All proposals appear to have in common that they are variants of a Wess-Zumino-Witten field theory. They predict strictly parabolic multifractal spectra $\tau_q$, which appears to be in conflict with existing numerics [9,10]. The earlier numerical results [9,10] have been questioned in recent analytical studies [7,8,11]: Building upon earlier work of Suslov [12], M. Zirnbauer and coauthors derived strict parabolicity at 2D localization-delocalization transitions for the Wigner-Dyson classes in a rigorous manner, invoking only conformal invariance and Abelian fusion. Taken at face value, the claim of strict parabolicity seems to carry over also to the non-standard symmetry classes (see [13] for a rigorous proof). Motivated by these developments, we have performed over the last couple of years an extensive numerical study of multifractality the integer (class A) and spin (class C) quantum Hall transitions [14,15]. Invoking an unprecedented numerical data quality together with new analysis tools, we confirm the main finding of previous numerics: significant deviations from parabolicity exist in classes A and C in contrast to the analytical predictions. For class C, consistent results have been found in Ref. [13], employing subleading multifractality as an alternative observable. Our findings are clearly inconsistent with the strict parabolicity predicted for “traditional” conformal field theories. We speculate that weak deviations from parabolicity as observed in our work and independently in Ref. [13] could be a manifestation of an underlying logarithmic CFT. [16,17] [1] M. R. Zirnbauer, arXiv:hep-th/9905054 (1999) [2] M. J. Bhaseen, I. Kogan, O. A. Soloviev, N. Taniguchi, and A. M. Tsvelik, Nucl. Phys. B 580, 688 (2000) [3] D. Bernard and A. LeClair, Nucl. Phys. B 628, 442 (2000) [4] A. M. Tsvelik; arXiv:cond-mat/0702611 (2007) [5] A. LeClair, arXiv:0710.3778v2 (2008) [6] Y. Ikhlef, P. Fendley, and J. Cardy, Phys. Rev. B 84, 144201 (2011) [7] M. Zirnbauer, Nucl. Phys. B 941, 458 (2019) [8] M. Zirnbauer, Ann. Phys. 431, 168559 (2021) [9] F. Evers, A. Mildenberger, and A. D. Mirlin, Phys. Rev. Lett. 101, 116803 (2008) [10] H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, and A. W. W. Ludwig, Phys. Rev. Lett. 101, 116802 (2008) [11] R. Bondesan, D. Wieczorek, and M. R. Zirnbauer, Nucl. Phys. B 918, 52 (2017) [12] I. M. Suslov, J. Exp. Theor. Phys. 128, 845 (2016) [13] J. F. Karcher, N. Charles, I. A. Gruzberg, and A. D. Mirlin, arXiv:2107.06414 [14] M. Puschmann, D. Hernangómez-Pérez, B. Lang, S. Bera, and F. Evers, Phys. Rev. B 103, 235167 (2021) [15] M. Puschmann, D. Hernangómez-Pérez, B. Lang, S. Bera, and F. Evers, work in progress. [16] J. Cardy, J. Phys. A 46, 494001 (2013) [17] V. Gurarie and A. W. W. Ludwig, “ From Fields to Strings: Circumnavigating Theoretical Physics”, pp. 1384-1440 (2005)

Many-body localized (MBL) phases of disordered quantum many-particle systems have a number of unique properties, including failure to act as a thermal bath and protection of quantum coherence. Studying MBL is complicated by the effects of rare ergodic regions, necessitating large system sizes and averaging over many disorder configurations. Here, building on the Feynman-Vernon theory of quantum baths, we characterize the quantum noise that a disordered spin system exerts on its parts via an influence matrix (IM). In this approach, disorder averaging is implemented exactly, and the thermodynamic-limit IM obeys a self-consistency equation. Viewed as a wavefunction in the space of trajectories of an individual spin, the IM exhibits slow scaling of temporal entanglement in the MBL phase. This enables efficient matrix product states computations to obtain temporal correlations, providing a benchmark for quantum simulations of non-equilibrium matter. The IM quantum noise formulation provides an alternative starting point for novel rigorous studies of MBL.

The phenomenon of many-body localization (MBL) is attracting significant theoretical and experimental interest over the past few years. The signatures of MBL have been observed in recent cold-atom experiments in optical lattices. The recent experimental advances of synthetic gauge fields allow us to explore the MBL with magnetic flux. We discuss the role of synthetic magnetic fields on the localization properties of disordered fermions. The spectral statistics exhibit a transition from ergodic to MBL phase, and the transition shifts to larger disorder strengths with increasing magnetic flux. The dynamical properties indicate the charge excitation remains localized whereas spin degree of freedom delocalized in the presence of synthetic flux. The full localization of spin excitation can be recovered when spin-dependent disorder potential is realized. Furthermore, we show the effect of quantum statistics on the local correlations and show that the long-time spin oscillations of a hard-core boson system are destroyed in contrast to the fermionic case.

We study the finite-temperature transport of electrons coupled to anharmonic local phonons. Our focus is on the high-temperature incoherent regime, where controlled calculations are possible both for weak and strong electron-phonon coupling. At strong coupling, the dynamics is described in terms of a multiple-species gas of small polarons. We explicitly compute the d.c. and a.c. response in this regime. We discuss the breakdown of the polaron picture and the onset of localization, in the limit where the phonons become quasistatic.

In the study of quantum thermalisation in isolated quantum many-body systems, the recently developed influence matrix (IM) approach has opened new doors for the efficient simulation of quantum many-body dynamics [1-4]. This approach is inspired by the Feynman-Vernon Influence Functional which encodes the dynamical influence of a many-body bath on a local subsystem [5]. While a self-consistant approach to the computation of the IM has been proven extremely versatile for the efficient application of MPS algorithms, this technique is not applicable to arbitrary initial states. I will present a complementary perspective in which the IM is viewed as generating functional for Keldysh correlation functions in the bath. By computing these correlation functions explicitly, the IM can be reconstructed for a large range of initial states and certain types of Floquet dynamics. Moreover, this perspective can serve as useful starting point for approximations and renormalisation group approaches which may help to shed new light on the mechanisms governing out-of-equilibrium quantum many-body dynamics. [1] Influence matrix approach to many-body Floquet dynamics (Lerose, Sonner, Abanin), Phys. Rev. X 11, 021040 (2021). [2] Characterizing many-body localization via exact disorder-averaged quantum noise (Sonner, Lerose, Abanin), arXiv:2012.00777 (2020). [3] Influence functional of many-body systems: temporal entanglement and matrix-product state representation (Sonner, Lerose, Abanin), Annals of Physics 431, 168552 (2021). [4] Scaling of temporal entanglement in proximity to integrability (Lerose, Sonner, Abanin), Phys. Rev. B 104, 035137 (2021). [5] The theory of a general quantum system interacting with a linear dissipative system (Feynman, Vernon), Annals of Physics 24, 118-173 (1963).

In this talk, I will outline the application of topological string theory to ergodic-to-nonergodic transitions in condensed matter theory. Such transitions, which include Anderson localization, lack a local order parameter; a situation which is reminiscent of topological phase transitions. Instead, the degree of ergodicity of a quantum system is exhibited by the statistics of its energy levels, as characterized by the spectral form factor (SFF). We calculate the SFF for a one-parameter family of matrix models which appeared as a phenomenological description of ergodic-to-nonergodic transitions. The same matrix model can be interpreted as a topological string theory on the cotangent space of the three-sphere. Using the theory of symmetric polynomials, we derive an analytical expression for the SFF; this result generalizes to all matrix models satisfying the assumptions of Szegö's limit theorem. In the Chern-Simons description of topological string theory, the SFF is proportional to the topological (HOMFLY) invariant of (2n,2)-torus links. We argue that the absence of a local order parameter suggests that it is natural to characterize ergodic-to-nonergodic transitions using topological tools, such as we have done here.

In recent years, locally interacting system with static disorder, such as e.g. a random-field Ising chain with nearest neighbor interactions, received much attention because they can exhibit many-body localization. Many-body localized systems fail to equilibrate locally under unitary time evolution due to the absence of transport and the emergence of quasi-local integrals of motions, and thus, retain information about the initial state in local observables. In our work, we explore the dynamics of a spin chain with a local antiferromagnetic interaction, and non-local spin-flip interactions induced by coupling of the spins to a central d-level system (qudit). We employ the multilayer multiconfiguration time-dependent Hartree approach [2,3] to simulate the dynamics of moderately large spin chains in a numerically exact way. Using this approach, we examine dynamical properties of the spin chain and the qudit, with particular focus on the question whether the system retains information about the initial state in local observables. [1] A. Pal et al., Phys. Rev. B 82, 174411 (2010) [2] H. Wang et al., J. Chem. Phys. 119, 1289 (2003) [3] O. Vendrell et al., J. Chem. Phys. 134, 044135 (2011)

We investigate the dynamics of entanglement of Many-Body Localized (MBL) systems coupled to various types of Markovian environments. We use the third R\'{e}nyi negativity $R_3$ as a proxy for mixed-state entanglement. This quantity can be efficiently computed using tensor-network techniques and reduces to the third R\'{e}nyi entropy when the system is isolated. Hence $R_3$ captures the characteristic logarithmic growth of interacting localized systems under a global quench, up to intermediate times where the effects of the environment coupling are not dominating the dynamics yet. Therefore it is a useful tool to distinguish interacting from non-interacting types of localization up to intermediate times, and to quantify entanglement in mixed-state dynamics.

Quantum many-body scars have been put forward as counterexamples to the Eigenstate Thermalization Hypothesis. These atypical states are observed in a range of correlated models as long-lived oscillations of local observables in quench experiments starting from selected initial states. The long-time memory is a manifestation of quantum non-ergodicity generally linked to a sub-extensive generation of entanglement entropy, the latter of which is widely used as a diagnostic for identifying quantum many-body scars numerically as low entanglement outliers. Here we show that, by adding kinetic constraints to a fractionalized orthogonal metal, we can construct a minimal model with orthogonal quantum many-body scars leading to persistent oscillations with infinite lifetime coexisting with rapid volume-law entanglement generation. Our example provides new insights into the link between quantum ergodicity and many-body entanglement while opening new avenues for exotic non-equilibrium dynamics in strongly correlated multi-component quantum systems. Reference: arXiv:2102.07672