Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session K33: Many-Body Localization |
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Sponsoring Units: DCMP Chair: Lingyuan Gao, University of Arkansas Room: Room 225 |
Tuesday, March 7, 2023 3:00PM - 3:12PM |
K33.00001: Many-Body Localization from the perspective of the Fock-Space propagator Subroto Mukerjee, Jagannath Sutradhar, Soumi Ghosh, Sthitadhi Roy, David E Logan, Sumilan Banerjee We implement a recursive Green's function method to extract the Fock space (FS) propagator and associated self-energy across the many-body localization (MBL) transition, for one-dimensional interacting fermions in a random on-site potential. We show that the typical value of the imaginary part of the local FS self-energy, Δt related to the decay rate of an initially localized state, acts as a probabilistic order parameter for the thermal to MBL phase transition and can be used to characterize critical properties of the transition as well as the multifractal nature of MBL states as a function of disorder strength W. In particular, we show that a fractal dimension Ds extracted from Δt jumps discontinuously across the transition, from Ds<1 in the MBL phase to Ds=1 in the thermal phase. Moreover, Δt follows an asymmetrical finite-size scaling form across the thermal-MBL transition, where a nonergodic volume in the thermal phase diverges with a Kosterlitz-Thouless–like essential singularity at the critical point Wc and controls the continuous vanishing of Δt as Wc is approached. In contrast, a correlation length (ξ) extracted from Δt exhibits a power-law divergence on approaching Wc from the MBL phase. We also comment on the similarities and differences between the form of the Fock space propagator for systems with disorder and those with quasiperiodic potentials. |
Tuesday, March 7, 2023 3:12PM - 3:24PM |
K33.00002: Phenomenology of the Prethermal Many-Body Localized Regime David M Long, Philip Crowley, Vedika Khemani, Anushya Chandran The dynamical phase diagram of interacting disordered systems has seen substantial revision over the past few years. Theory must now account for a large prethermal many-body localized (MBL) regime in which thermalization is extremely slow, but not completely arrested. We derive a quantitative description of these dynamics in short-ranged one-dimensional systems using a model of successive many-body resonances. The model explains the decay timescale of mean autocorrelators, the functional form of the decay––a stretched exponential––and relates the value of the stretch exponent to the broad distribution of resonance timescales. The Jacobi method of matrix diagonalization provides numerical access to this distribution, as well as a conceptual framework for our analysis. The resonance model correctly predicts the stretch exponents for several models in the literature. Successive resonances may also underlie slow Floquet heating, and slow thermalization in strongly disordered systems in higher dimensions, or with long-range interactions. |
Tuesday, March 7, 2023 3:24PM - 3:36PM |
K33.00003: Analysis of many-body localization from different perspectives David A Zarate-Herrada, Lea F. Santos, E. Jonathan Torres-Herrera Finite-size effects have been a major and justifiable source of concern in the analysis of many-body localization. Another crucial problem, that is sometimes overlooked, is the lack of self-averaging and the consequent danger of reducing the number of random realizations as the system size increases. In our work, we take into account the issue of self-averaging and investigate how different quantities, that are used to determine the possible transition from an ergodic to a many-body localized phase, depend on system size. Our analysis focuses on the one-dimensional spin-1/2 Heisenberg model with onsite disorder. We find that level statistics, structure of the eigenstates, and dynamics may lead to contradictory results. For a fixed disorder strength, one quantity may indicate chaos enhancement as the system size increases, while another one may suggest approach to a localized phase. |
Tuesday, March 7, 2023 3:36PM - 3:48PM |
K33.00004: Scattering Expansion for Localization in One Dimension Adrian B Culver, Pratik Sathe, Rahul Roy We present a perturbative approach to a broad class of disordered systems in one spatial dimension. Considering a long chain of identically disordered scatterers, we expand in the reflection strength of any individual scatterer. This expansion accesses the full range of phase disorder from weak to strong. As an example application, we show analytically that in a discrete-time quantum walk, the localization length can depend non-monotonically on the strength of phase disorder (whereas expanding in weak disorder yields monotonic decrease). Returning to the general case, we obtain to all orders in the expansion a particular non-separable form for the joint probability distribution of the log-transmission and reflection phase. Furthermore, we show that for weak local reflection strength, a version of the scaling theory of localization holds: the joint distribution is determined by just three parameters. |
Tuesday, March 7, 2023 3:48PM - 4:00PM |
K33.00005: Dynamics of quantum avalanches in 1D disordered spin chains J. Clayton Peacock, Dries Sels Recent studies have questioned the stability of the many-body localized (MBL) phase in one-dimensional disordered spin chains in the thermodynamic limit. Thermalization in this limit is thought to be due to "quantum avalanches", in which rare Griffiths regions of lower disorder serve as thermalizing baths. These regions, which are sure to exist in the thermodynamic limit, are rare by nature and thus to observe their effect one either needs to access very large system sizes or resort to biased sampling. In this talk we present evidence of avalanches in numerical studies using the latter, and show these systems are unstable at disorder much larger than commonly believed. |
Tuesday, March 7, 2023 4:00PM - 4:12PM |
K33.00006: Looking inside the avalanche in a many-body localization model Hyunsoo Ha, David A Huse, Alan Morningstar Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, non-integrable, and in a highly-excited state. One instability of MBL systems is the so-called ``avalanche'', where a locally thermalizing region is able to spread thermalization through the full system. The avalanche may be modeled and numerically studied in finite one-dimensional systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via rare ``bottleneck" eigenstates of the closed system. These rare eigenstates are involved in exceptionally strong many-body resonances that are put ``on shell" by the bath. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL. |
Tuesday, March 7, 2023 4:12PM - 4:24PM |
K33.00007: Avalanche stability transition in interacting quasiperiodic systems Yi-Ting Tu, DinhDuy Vu Coupling a 1D quasiperiodic interacting system to a Markovian bath, we study the avalanche instability of the many body localized phase numerically, finding that many body localization (MBL) likely exists in pseudorandom quasiperiodic systems in the thermodynamic limit for a disorder strength W>8 (to be compared with W>18 in the corresponding randomly disordered case). We support our conclusion by additionally developing real space RG arguments, and provide a detailed comparison between quasiperiodic and random MBL from the avalanche instability perspective, concluding that the two belong to different universality classes. |
Tuesday, March 7, 2023 4:24PM - 4:36PM |
K33.00008: Stark many-body localization in spin chains with single-ion anisotropy Edson Vernek, Márcio G Sousa, Rafael F Costa The interesting phenomena of many-body localization (MBL) has attracted a great deal of attention in condensed matter physics. Resulting from the intricate role of disorder in the dynamics of quantum states, one of the physical consequences is that if the system is initially in some non-equilibrium quantum state, it does not thermalize upon time evolution. This so-called localized regime is predicted to exist in a variety of systems. It has been shown that localization can be obtained even without disorder [1]. In this case, the localization is promoted by a nearly uniform gradient potential across an interacting quantum system and the phenomenon is termed Stark man-body localization (SMBL). |
Tuesday, March 7, 2023 4:36PM - 4:48PM |
K33.00009: Symmetries and Delocalization in the Disordered Hubbard Model Steven Thomson Many-body localization is believed to be generically unstable in quantum systems with continuous non-Abelian symmetries, even in the presence of strong disorder. Breaking these symmetries can stabilise the localized phase, leading to the emergence of an extensive number of quasi-locally conserved quantities known as local integrals of motion, or l-bits. Using a sophisticated non-perturbative technique based on continuous unitary transforms, we investigate the one-dimensional Hubbard model subject to both spin and charge disorder, compute the associated l-bits and demonstrate that the disorder gives rise to a novel form of spin-charge separation. We examine the role of symmetries in delocalizing the spin and charge degrees of freedom, and show that while symmetries generally lead to delocalization through multi-particle resonant processes, certain subsets of states appear stable. |
Tuesday, March 7, 2023 4:48PM - 5:00PM |
K33.00010: Absence of localization in interacting spin chains with a discrete symmetry Benedikt Kloss, Jad C Halimeh, Achilles Lazarides, Yevgeny Bar Lev We prove that spin chains symmetric under a combination of mirror and spin-flip symmetries and with a nondegenerate spectrum show finite spin transport at zero total magnetization and infinite temperature. We demonstrate this numerically using two prominent examples: the Stark many-body localization system and the symmetrized many-body localization system. We provide evidence of delocalization at all energy densities and show that the delocalization mechanism is robust to breaking the symmetry. We use our results to construct two localized systems which, when coupled, delocalize each other. |
Tuesday, March 7, 2023 5:00PM - 5:12PM |
K33.00011: Localization-delocalization transition in many-body quantum systems with correlated disorder E. Jonathan Torres-Herrera, Isaías Vallejo The presence of frozen uncorrelated random on-site potential in interacting quantum systems can induce a transition from an ergodic phase to a localized one, the so-called many-body localization. Here we numerically study the effects of auto-correlated disorder on the static and dynamical properties of a one-dimensional many-body quantum system which exhibits many-body 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 on-site potentials in the one-dimensional spin-1/2 Heisenberg model leads to suppression of the many-body localization phase, while level repulsion is mitigated for small disorder strengths, although energy eigenstates remain well extended. Our findings are also remarkably manifested in time domain, on which we put main emphasis, as shown by the time evolution of experimentally relevant observables, like the return probability and the spin auto-correlation function. |
Tuesday, March 7, 2023 5:12PM - 5:24PM |
K33.00012: Incommensurate many-body localization in the presence of long-range hopping and single-particle mobility edge Ke Huang, DinhDuy Vu, Xiao Li Single-particle lattice model can possess an intermediate phase with coexisting extended and localized states separated by a single-particle mobility edge (SPME). To investigate the role of SPME in the presence of short-range interactions, we specifically study the $t_1$-$t_2$ model, namely the Aubry-Andre (AA) model with next-nearest-neighbor (NNN) hopping. For weak interactions ($Ull t_1$), the system preserves its single-particle properties, resulting in the distinction between the AA and the $t_1$-$t_2$ model. However, for intermediate interactions ($Usim t_1$), two models exhibit qualitatively similar thermal-MBL transition, which agrees with the experimental observations. Additionally, for strong interactions ($Ugg t_1$), the two models are disparate because the NNN hopping breaks down the Hilbert space fragmentation in the AA model. We anticipate that the phenomena for weak and intermediate interactions are generic for models with SPME, while the breakdown in the strong-interaction regime is limited to the $t_1$-$t_2$ model. |
Tuesday, March 7, 2023 5:24PM - 5:36PM |
K33.00013: Nonequilibrium Dynamics Of Correlated Disordered Systems, An Effective Medium Approach Herbert F Fotso Although most studies of strongly correlated systems away from equilibrium have focussed on clean systems, it is well known that disorder can affect these dynamics in various nontrivial ways. In this talk, we discuss our recently introduced solution for the nonequilibrium dynamics of an interacting disordered system[1]. This approach adapts the combination of the equilibrium dynamical mean field theory (DMFT) and the equilibrium coherent potential approximation (CPA) methods to the nonequilibrium many-body formalism, for the dynamics of interacting disordered systems away from equilibrium. The time domain solution can be used to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for the cumbersome analytical continuation process. We demonstrate the application of the nonequilibrium solution to the interaction quench problem for an isolated disordered system. Here, the interaction is abruptly changed from zero to another constant (finite) value at which it is subsequently kept. We observe, via the time-dependence of different physical observables, the effect of disorder on the relaxation of the system as a function of final interaction strength. This real-time characterization has the potential to shed new light on the fundamental role of disorder in the nonequilibrium dynamics of interacting quantum systems. |
Tuesday, March 7, 2023 5:36PM - 5:48PM |
K33.00014: Thermalization and localization in discretized quantum field theory Spasen Chaykov, Brenden M Bowen, Nishant Agarwal The von Neumann entanglement entropy of a sub-region in an out-of-equilibrium many-body quantum system evolves in time. For the late-time steady state, a “volume” law behavior typically indicates thermalization, whereas memory of the initial state (such as an “area” law behavior) may indicate localization. In this talk, I will discuss these two phases in the context of discretized scalar quantum field theory in two and four spacetime dimensions in the absence/presence of disorder. I will restrict to Gaussian initial states with linear dynamics and obtain exact results using the covariance matrix (whose dimension scales linearly with system size). I will first review the results for a mass quench in the free theory where the entanglement entropy grows linearly in time, saturating to a volume law behavior. I will next introduce a local disorder term in the Hamiltonian and show that, for sufficiently large disorder strength, the growth of entanglement entropy is suppressed, preserving the initial state behavior. I will finally discuss the continuum limit and how it affects measures such as the gap ratio. |
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