Bulletin of the American Physical Society
2024 APS March Meeting
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session Y14: ManyBody Localization 
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Sponsoring Units: DCMP Chair: E. Jonathan TorresHerrera, Institute of Physics, BUAP Room: M100E 
Friday, March 8, 2024 8:00AM  8:12AM 
Y14.00001: Operator growth in Many Body Localized systems J. Clayton Peacock, Dries Sels There has been recent attention to the use of the Lanczos recursion method in characterizing chaotic systems. Operators evolve in time under the Louivillian superoperator. The recursion method builds a Krylov basis with repeated application of the Louivillian, and outputs a sequence of positive numbers called the “Lanczos coefficients” and an orthonormal basis for the Krylov space. In this basis, the Louivillian is tridiagonal with the Lanczos coefficients on the offdiagonals.
These coefficients parametrize the growth of complexity of the operator used to generate them. In this talk, I will analyze the behavior of these coefficients in large disordered XXZ spin chains, in regimes often characterized as manybody localized. I will look at their behavior both with and without an added thermal inclusion (region of much lower average disorder) and provide evidence for the absence of localization.

Friday, March 8, 2024 8:12AM  8:24AM 
Y14.00002: Propagation of avalanches in the disordered Heisenberg model: a computational study Tomasz Szoldra, Piotr Sierant, Jakub Zakrzewski, Maciej A Lewenstein The transition from ergodic to manybody localized phases is believed to be driven by an avalanche mechanism. In this process, thermalized regions form due to disorder fluctuations, promoting thermalization of their vicinity and consequent system delocalization, unless the disorder strength is sufficient to inhibit this process. We consider the XXZ model with uniform disorder in contact with a weakly disordered spin chain, comprising a finite thermal bath. By inspecting the time evolution of the twobody spin correlation functions with the bath, we are able to capture thermal avalanches spreading through the system, or a lack thereof, depending on the disorder strengths and system sizes. We also confirm that a weakly disordered bath Hamiltonian can be well approximated by a Gaussian Orthogonal Ensemble random matrix upon a proper energy rescaling. Finally, we comment on the recent result of Peacock and Sels (PRB 108, L020201 (2023)), noticing that a universal thermalizing behavior caused by a thermal inclusion may be an effect of the lack of energy conservation and our numerics suggests it does not occur for a timeindependent Hamiltonian. 
Friday, March 8, 2024 8:24AM  8:36AM 
Y14.00003: Time crystal in nonHermitian system Weihua Xie, Michael Kolodrubetz Time crystals are an interesting new nonequilibrium phase of matter formed by repeating patterns in time, featuring timetranslation symmetry breaking. Recently, Basu et al. [1] have opened the door to more interesting forms of symmetry breaking by nonunitary dynamics, such as a time crystal with quasilongrange order. We consider an interacting form of this model and numerically solve it via time evolving block decimation (TEBD), comparing this to an analytical treatment via meanfield theory. Our findings, both numerical and analytical, consistently show that considering integrability breaking interactions will shift the phase diagram but maintain the existence of the quasi time crystal phase for weak interactions. One intriguing discovery from numeric is the emergence of a new phase transition appearing to be associated with a new, unexpected symmetry breaking. We comment on progress understanding this additional symmetry breaking. 
Friday, March 8, 2024 8:36AM  8:48AM 
Y14.00004: Entanglement growth and localization in the disordered Fermi Hubbard model Rachel Wortis Manybody localization impedes the spread of information encoded in initial conditions, blocking (or at least radically slowing) thermalization of an isolated quantum system. We examine the potential to tailor the growth of entanglement in the Fermi Hubbard model by tuning disorder in both the charge and spin degrees of freedom. We begin by expressing the Hamiltonian in terms of a set of optimally localized conserved quantities, and examine in detail the growth of entanglement entropy and its connection with the coupling between these local integrals of motion. We demonstrate how the strength of the disorder in charge and in spin controls the time scales seen in entanglement growth. We also show a shift in behaviour between the weakly and strongly interacting limit in which local integrals of motion lose their close association with Anderson localized singleparticle states. 
Friday, March 8, 2024 8:48AM  9:00AM 
Y14.00005: Geometric Characterization of ManyBody Localization William N Faugno, Tomoki Ozawa Manybody localization (MBL) is the breaking of ergodicity in disordered interacting systems wherein all eigenstates localize. MBL is interesting both for understanding the fundamental physics of thermalization and for potential applications as quantum memory. MBL was originally characterized by its entanglement entropy evolution and system size scaling. As a localized phase, it is natural to characterize states by their localization length. Indeed, phenomenological models of MBL propose a set of local integrals that lead to a hierarchy of length scales. To present, there have been a variety of localization lengths defined typically based in part on Fock space localization. Here we attempt to extract a real space localization length through the manybody quantum metric (MBQM), which has been defined in the development of the modern theory of insulators and shown to be related to the positional variance in single particle systems. We study the onedimensional disorder FermiHubbard model. We find that the MBQM can indeed be used to characterize the phase transition and construct a phase diagram as a function of disorder strength and interaction strength. We also find that the MBQM gives rise to a natural localization length in the thermodynamic limit. 
Friday, March 8, 2024 9:00AM  9:12AM 
Y14.00006: Localization spectrum of a bathcoupled generalized AubryAndré model in the presence of interactions YiTing Tu, DinhDuy Vu A generalization of the AubryAndré model, the noninteracting GaneshanPixleyDas Sarma model (GPD) introduced by Ganeshan et al. [Phys. Rev. Lett. 114, 146601 (2015)], is known analytically to possess a mobility edge, allowing both extended and localized eigenstates to coexist. This mobility edge has been hypothesized to survive in closed manybody interacting systems, giving rise to a new nonergodic metallic phase. In this work, coupling the interacting GPD model to a thermal bath, we provide direct numerical evidence for multiple qualitative behaviors in the parameter space of disorder strength and energy level. In particular, we look at the bathinduced saturation of entanglement entropy to classify three behaviors: thermalized, nonergodic extended, and localized. We also extract the localization length in the localized phase using the longtime dynamics of the entanglement entropy and the spin imbalance. Our work demonstrates the rich localization landscape of generalized AubryAndré models containing mobility edges in contrast to the simple AubryAndré model with no mobility edge. 
Friday, March 8, 2024 9:12AM  9:24AM 
Y14.00007: Interactionenhanced many body localization in a generalized AubryAndre model Ke Huang, DinhDuy Vu, Xiao Li In Ref. [1], we study the manybody localization (MBL) transition in a generalized AubryAndre model (also known as the GPD model) introduced in Ref. [2]. In contrast to MBL in other disordered or quasiperiodic models, interaction seems to unexpectedly enhance MBL in the GPD model in some parameter range. To understand this counterintuitive result, we demonstrate that the highestenergy singleparticle band in the GPD model is unstable against even infinitesimal disorder, which leads to this surprising MBL phenomenon in the interacting model. We develop a meanfield theory description to understand the coupling between extended and localized states, which we validate using extensive exact diagonalization and DMRGX numerical results. 
Friday, March 8, 2024 9:24AM  9:36AM 
Y14.00008: Time evolution around the manybody localization transition: Effects of autocorrelated disorder E. Jonathan TorresHerrera, Isaías Vallejo The presence of frozen uncorrelated random onsite potential in interacting quantum systems can induce a transition from an ergodic phase to a localized one, the socalled manybody localization. Here we numerically study the effects of autocorrelated disorder on the static and dynamical properties of a onedimensional manybody quantum system which exhibits manybody localization. Specifically, by means of some standard measures of energy level repulsion and localization of energy eigenstates, we show that a strong degree of correlations between the onsite potentials in the onedimensional spin1/2 Heisenberg model leads to suppression of the manybody localization phase, while level repulsion is mitigated for small disorder strengths, although energy eigenstates remain well extended. Our findings are also remarkably manifested in the time domain, on which we put the main emphasis, as shown by the time evolution of experimentally relevant observables, like the return probability and the spin autocorrelation function. 
Friday, March 8, 2024 9:36AM  9:48AM 
Y14.00009: NonHermitian ManyBody Localization Through Singular Value Decomposition Federico Roccati, Federico Balducci, Ruth Shir, Aurelia Chenu A hallmark of disordered manybody interacting quantum systems are manybody localized (MBL) regimes. A strong quenched disorder can suppress the resonant processes responsible for the transport of particles or energy. Thus, MBL is considered a consequence of unitary evolution, and it is expected to be washed away when coupling the system to an environment. The study of the interplay of dissipation and MBL has been a topic of recent interest, in particular thanks to the advancements in nonHermitian (NH) physics [14]. NH Hamiltonians are used as an effective tool to describe dissipation in open quantum systems, and are derived from a GKSL master equation for nullmeasurement conditioning (nojump trajectories). However, most studies up to date focused on standard MBL Hamiltonians, subjected to a uniform dissipation. In this work, we take a different perspective and investigate whether random dissipation can induce NH localization in an otherwise clean manybody system. We propose the use of the singular value decomposition, motivated by recent works in nonHermitian physics [56], as the right tool to diagnose MBL in a nonHermitian setting. Within this context, we find that an inhomogeneous nonHermiticity induces a form of manybody localization [7], with the same confidence with which localization is seen in similar Hermitian systems. 
Friday, March 8, 2024 9:48AM  10:00AM 
Y14.00010: Spin Survival Probability as a Probe of Dynamics in InfiniteTemperature Strongly BondDisordered 1D Chains Yi Zhao, Joel E Moore The onsite survival probability of an initially oriented spin as a function of time in infinitetemperature, or equivalently randomly initialized, disordered systems has become accessible in various experimental settings. Certain universal properties are computable in onedimensional disordered systems using the formalism of the strongdisorder renormalization group (SDRG). We show that, even at very strong disorder, SDRG is only capable of predicting the longtime asymptotic approach of this function rather than its value at infinite time, the latter being sensitive to the precise structure of the localized eigenfunctions. We corroborate this result with extensive numerical studies for the nearestneighbor bonddisordered XX spin chain. We also extend our investigation to onedimensional spin chains with longrange interactions under positional disorder: while no SDRG approach appears available for such models, numerical results for the survival probability at accessible system sizes suggest the same form of longtime asymptotic approach. We comment on possible ways in which the survival probability may probe manybody localization. 
Friday, March 8, 2024 10:00AM  10:12AM 
Y14.00011: Nonequilibrium dynamics of correlated quantum systems in the presence of disorder Herbert F Fotso The interplay of interaction and disorder gives rise in equilibrium to a vast array of intriguing properties and has thus rightfully received a great deal of attention. Away from equilibrium however, the transient dynamics of manyparticle systems that feature both interaction and disorder is rather challenging despite this significant interest. In this talk, we introduce our recently developed nonequilibrium DMFT+CPA embedding scheme, that combines both the dynamical mean field theory (DMFT) and the coherent potential approximation (CPA) nonequilibrium extensions, to characterize the dynamics of a disordered interacting system described by the AndersonHubbard model under a timedependent interaction [1]. We consider various types of disorder and analyze the thermalization of the system in particular under an interaction quench. Our studies show that disorder can tune the final temperature of the system across a broad range of values depending on the interaction strength [2]. [1] Eric Dohner, Hanna Terletska, KaMing Tam, Juana Moreno, Herbert F. Fotso, "Nonequilibrium DMFT+CPA for Correlated Disordered Systems", Phys. Rev. B 106 195156 (2023). [2] Eric Dohner, Hanna Terletska, Herbert F. Fotso, "Thermalization of a Disordered Interacting System under an Interaction Quench", Phys. Rev. B 108, 144202 (2023). 
Friday, March 8, 2024 10:12AM  10:24AM 
Y14.00012: Local Integrals of Motion in Anderson and ManyBody Localized Phases Jesko Sirker, Alexander Weisse, Robert Gerstner We discuss general bounds for the growth of local operators under Hamiltonian dynamics. We point out fundamental differences between the case of an Anderson localized phase and the putative case of manybody localization. Our results are consistent with recent findings that localization does not occur in the manybody case. 
Friday, March 8, 2024 10:24AM  10:36AM 
Y14.00013: Thermalization dynamics in a glassy quantum circuit Richard D Barney, Yunxiang Liao, Victor M Galitski Quantum circuits have emerged as a useful setting for studying quantum manybody systems. Random quantum circuits have been particularly useful in examining chaotic behavior in these systems and identifying its universal features. In this talk we present a random Floquet circuit model that is neither integrable nor fully chaotic, instead exhibiting glassy behavior. In general it quickly thermalizes within a sector of the state space but only fully thermalizes at a much later time, if at all. Using an effective field theory approach we determine the ensembleaveraged time evolution of the density matrix and the twolevel correlation function. We demonstrate that these results indicate a glassy twostep thermalization process. 
Friday, March 8, 2024 10:36AM  10:48AM 
Y14.00014: Dynamically Frozen Floquet Quantum Matter: Ergodicity Breaking without Disorder in the Thermodynamic Limit Asmi Haldar Ergodicity is at the heart of equilibrium Statistical Mechanics. The hypothesis has immediate implications in predicting generic behaviour of a system driven out of equilibrium. For example, ergodicity hypothesis implies, when a clean, quantum chaotic, manybody system is driven by varying a parameter of its Hamiltonian periodically in time, the system will heat up without bound. In the absence of any conservation law, the drive is expected to steer it towards a chaotic state described locally by an infinitetemperature ensemble. Here we present a generic counterexample to this premise. We show, a manybody system under strong periodic drive can dynamically freeze into nontrivial states due to emergence of certain approximate but perpetual conservation laws. As a striking demonstration, an infinite, clean, interacting, nonintegrable manybody system is shown to exhibit zero growth of entanglement entropy density after being driven over several decades. Several aspects of the phenomena, including the energence of the conservation laws, pose new open puzzles that cannot be explained by conventional concepts. We will outline those in the talk. 
Friday, March 8, 2024 10:48AM  11:00AM 
Y14.00015: Analytically quantifying cat scar enforced discrete time crystalline orders Biao Huang We construct an analytical perturbation theory to quantitatively characterize rare Schrodinger's cat eigenstates, dubbed cat scars, in a Floquet system. The theory allows for computing the analytical scaling relations for their associated discrete time crystal (DTC) dynamics, including DTC amplitude, Fock space localization, and DTC lifetime scaling. In particular, we show that a plethora of inhomogeneous cat eigenstate configurations can be precisely engineered using a minimal number of different twoqubit gates for interactions. Thus, our theory allows for deterministically enhancing the resource usage efficiency when engineering cat scar enforced DTCs in current noisyintermediatescalequantum devices. Further, the analytical framework sheds light on several subtle issues. They include the conditions to avoid Floquet manybody resonances in systems with strong Ising interactions, and the practical methods to verify genuine cat eigenstate enforced manybody DTCs. Relevant experiments on observing unconventional cat state dynamics in a catscarred DTC will also be discussed. 
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