Nonequilibrium dynamics in isolated quantum many-body systems displays a number of intriguing features, such as many-body localization (MBL) and prethermalization. Here we investigate a simple ladder system with disorder, in which various distinct dynamical features coexist and interplay. By exact diagonalization, we demonstrate that the system exhibits the signatures of an MBL-ergodic-MBL reentrant transition, metastability, and disorder-free MBL. We give an account of these properties by introducing a quasiparticle picture and interpreting the quasivacuum energy fluctuation as an effective disorder on the quasi-particle dynamics. It is speculated that the weak perturbation behavior is a finite-size effect, but its relaxation timescale increases with the system size.
Nonequilibrium dynamics in isolated quantum many-body systems displays a number of intriguing features, such as many-body localization (MBL) and prethermalization. Here we investigate a simple ladder system with disorder, in which various distinct dynamical features coexist and interplay. By exact diagonalization, we demonstrate that the system exhibits the signatures of an MBL-ergodic-MBL reentrant transition, metastability, and disorder-free MBL. We give an account of these properties by introducing a quasiparticle picture and interpreting the quasivacuum energy fluctuation as an effective disorder on the quasi-particle dynamics. It is speculated that the weak perturbation behavior is a finite-size effect, but its relaxation timescale increases with the system size.
In this paper, we develop a self-consistent Hartree-Fock approach to theoretically study the far-from-equilibrium quantum dynamics of interacting fermions, and apply this approach to explore the onset of many-body localization (MBL) in these systems. We investigate the dynamics of a state with a nonequilibrium density profile; we find that at weak disorder the density profile equilibrates rapidly, whereas for strong disorder it remains frozen on the accessible timescales. We analyze this behavior in terms of the Hartree-Fock self-energy. At weak disorder, the self-energy fluctuates strongly and can be interpreted as a self-consistent noise process. By contrast, at strong disorder the self-energy evolves with a few coherent oscillations which cannot delocalize the system. Accordingly, the nonequilibrium site-resolved spectral function shows a broad spectrum at weak disorder and sharp spikes at strong disorder. Our Hartree-Fock theory incorporates spatial fluctuations and rare-region effects. As a consequence, we find subdiffusive relaxation in random systems; but, when the system is subjected to weak quasiperiodic potentials, the subdiffusive response ceases to exist, as rare region effects are absent in this case. This self-consistent Hartree-Fock approach can be regarded as a relatively simple theory that captures much of the MBL phenomenology.
It is known that strong disorder in closed quantum systems leads to many-body localization (MBL), and that this quantum phase can be destroyed by coupling to an infinitely large Markovian environment. However, the stability of the MBL phase is less clear when the system and environment are of finite and comparable size. Here, we study the stability and eventual localization properties of a disordered Heisenberg spin chain coupled to a finite environment, and extensively explore the effects of environment disorder, geometry, initial state, and system-bath coupling strength, using the steady-state value of magnetization as a probe. Focusing on nonequilibrium dynamics and steady-state properties, our results indicate that within system sizes amenable to exact diagonalization, a strongly localized system interacting in a junction configuration retains remnant information on its initial state at long times despite coupling to a finite ergodic environment. In contrast, in a ladder configuration, strong dependencies on the initial state and coupling strength are observed, which can lead to either the loss or retention of information. Finally, we highlight and discuss discrepancies that can arise when similar methodologies are employed to infer localization or thermalization, revealing the need for careful interpretation.
We propose a Gaussian disorder to study many-body localization (MBL) in one-dimensional quantum system and coupled system-environment models. Unlike uniform disorder, Gaussian disorder is controlled by the standard deviation σ (driving MBL transitions) and the mean μ (causing global energy shifts). By calculating the von Neumann entropy, mean gap ratio, and dynamical indicators, we elucidate the ergodic-to-MBL transition as σ , with Gaussian disorder exhibiting more pronounced finite-size critical point drift effects compared to conventional random disorder. Through finite-size scaling analysis, it shows that there are no significant differences between the two disorder types at our assumed system sizes. We construct two system-environment coupling configurations (ladder and staggered), showing that under weak coupling, the system and environment evolve independently, whereas strong coupling induces cooperative localization. The ladder configuration shows a strong dependence on the initial state, which may lead to either the loss or retention of information, while no such dependence is observed in the staggered configuration. This can be explained by the changes in energy density of the initial state caused by variations in different model structures. When treating the system-environment as a unified two-dimensional ladder, asymmetric disorder on the two chains can drive a global MBL phase transition, with slightly different behaviors compared to symmetric disorder. Additionally, we emphasize the necessity of correctly selecting the initial state when characterizing the phase transition through dynamic indicators.
Recently it has been suggested that many-body localization (MBL) can occur in translationally-invariant systems, and candidate 1D models have been proposed. We find that such models typically exhibit strong finite-size effects due to the presence of two or more vastly different energy scales, including an artificial separation of density of states into bands separated by large energy gaps. By carefully choosing the parameters of the models such that finite-size effects are minimized, we perform extensive numerical studies of small systems using exact diagonalization. Based on the variety of diagnostics, including entanglement properties and the behavior of local observables, we find the systems exhibit thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translationally-invariant systems with two very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.
Abstract The connection between entanglement dynamics and non-equilibrium statistics in isolated many-body quantum systems has been established both theoretically and experimentally. Many-body localization (MBL), a phenomenon where interacting particles in disordered (i.e. random) chains fail to thermalize, exemplifies this connection. However, the systematic proof of critical phenomena such as MBL remains challenging due to the lack of robust methods for analyzing many-body entanglement dynamics. In this paper, we identify MBL through quasi-periodic dynamics in the entanglement evolution of subsystems in a disordered Heisenberg chain. This new form of characterizing MBL, through stable quasi-periodic dynamics of entanglement-where ‘stable’ means they persist in the thermodynamic limit—concretely distinguishes between two competing scenarios: fully localized behavior of subsystems or slowly, exponentially slow in disorder, thermalizing subsystems—a heated controversy in the literature. Utilizing perturbation theory, we derive the entanglement dynamics of single spins through an infinite perturbative series, while also modeling rare Griffiths regions (locally thermal inclusions). Our results prove that in regimes of sufficiently strong disorder, the entanglement evolution of individual subsystems remains quasi-periodic in the thermodynamic limit, thereby providing concrete evidence for the stability of MBL dynamics in disordered Heisenberg chains. This behavior contrasts with the widely reported logarithmic growth of subsystem entanglement in the MBL phase. We show that the logarithmic growth observed in prior studies arises from statistical ensemble averaging, which is prohibited due to the intrinsic non-ergodic dynamics characteristic of MBL systems, rooted in their quasi-periodic features.
Many-body localization(MBL) provides a mechanism by which isolated interacting quantum systems with disorder can avoid thermalization unlike ergodic systems satisfying the eigenstate thermalization hypothesis(ETH). Many-body localized systems retain signatures of their initial conditions at long times, whereas systems obeying ETH lose such information as they approach thermal equilibrium. Studying Non-equilibrium dynamics across ETH-MBL crossover is an important problem in condensed matter physics. Adiabatic control of parameters in interacting disordered systems provides a powerful framework to investigate MBL phases and their dynamical robustness. Using exact diagonalization and time-dependent numerical methods we study the effects of adiabatically ramped interactions in a disordered spin-1/2 XXZ chain, a paradigmatic model for exploring the many-body localization transition. By monitoring diagonal entropy density and entanglement entropy density growth across various ramp speeds, and system sizes. Our study incorporates Finite-size effects of spectral observables to probe the transition between ergodic and localized phases. The numerical results show that localized dynamical behavior remains largely intact under sufficiently slow ramp evolution, while increasing the driving rate promotes stronger excitation generation and larger entropy growth. This trend highlights the strong dependence of nonequilibrium adiabatic dynamics in disordered interacting quantum many-body systems.