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arXiv:1903.07338 · Physical Review Letters

Bath-Induced Decay of Stark Many-Body Localization

Ling-Na Wu, André Eckardt

Published Jul 18, 2019• 41 citations
arXivHTMLPDF

Abstract

We investigate the relaxation dynamics of an interacting Stark-localized system coupled to a dephasing bath, and compare its behavior to the conventional disorder-induced many body localized system. Specifically, we study the dynamics of population imbalance between even and odd sites, and the growth of the von Neumann entropy. For a large potential gradient, the imbalance is found to decay on a timescale τ that grows quadratically with the Wannier-Stark tilt. For the noninteracting system, it shows an exponential decay, which becomes a stretched exponential decay in the presence of finite interactions. This is different from a system with disorder-induced localization, where the imbalance exhibits a stretched exponential decay also for vanishing interactions. As another clear qualitative difference, we do not find a logarithmically slow growth of the von Neumann entropy as it is found for the disordered system. Our findings can immediately be tested experimentally with ultracold atoms in optical lattices.

DOI
10.1103/physrevlett.123.030602

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We investigate the relaxation dynamics of an interacting Stark-localized system coupled to a dephasing bath, and compare its behavior to the conventional disorder-induced many body localized system. Specifically, we study the dynamics of population imbalance between even and odd sites, and the growth of the von Neumann entropy. For a large potential gradient, the imbalance is found to decay on a timescale τ that grows quadratically with the Wannier-Stark tilt. For the noninteracting system, it shows an exponential decay, which becomes a stretched exponential decay in the presence of finite interactions. This is different from a system with disorder-induced localization, where the imbalance exhibits a stretched exponential decay also for vanishing interactions. As another clear qualitative difference, we do not find a logarithmically slow growth of the von Neumann entropy as it is found for the disordered system. Our findings can immediately be tested experimentally with ultracold atoms in optical lattices.
We study the relaxation dynamics of an extended Fermi-Hubbard chain with a strong Wannier-Stark potential tilt coupled to a bath. When the system is subjected to dephasing noise, starting from a pure initial state the system's total von Neumann entropy is found to grow monotonously. The scenario becomes rather different when the system is coupled to a thermal bath of finite temperature. Here, for sufficiently large field gradients and initial energies, the entropy peaks in time and almost reaches its largest possible value (corresponding to the maximally mixed state), long before the system relaxes to thermal equilibrium. This entropy peak signals an effective prethermal memory loss and, relative to the time where it occurs, the system is found to exhibit a simple scaling behavior in space and time. By comparing the system's dynamics to that of a simplified model, the underlying mechanism is found to be related to the localization property of the Wannier-Stark system, which favors dissipative coupling between eigenstates that are close in energy.
We study the relaxation dynamics of an extended Fermi-Hubbard chain with a strong Wannier-Stark potential tilt coupled to a bath. When the system is subjected to dephasing noise, starting from a pure initial state the system's total von Neumann entropy is found to grow monotonously. The scenario becomes rather different when the system is coupled to a thermal bath of finite temperature. Here, for sufficiently large field gradients and initial energies, the entropy peaks in time and almost reaches its largest possible value (corresponding to the maximally mixed state), long before the system relaxes to thermal equilibrium. This entropy peak signals a prethermal memory loss and, relative to the time where it occurs, the system is found to exhibit a simple scaling behavior in space and time. By comparing the system's dynamics to that of a simplified model, the underlying mechanism is found to be related to the localization property of the Wannier-Stark system, which favors dissipative coupling between eigenstates that are close in energy.
We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the noninteracting case, due to Wannier-Stark localization, the single-particle wave functions are exponentially localized even though the model has no quenched disorder. We show that this system remains localized in the presence of interactions and exhibits physics analogous to models of conventional many-body localization (MBL). In particular, the entanglement entropy grows logarithmically with time after a quench, albeit with a slightly different functional form from the MBL case, and the level statistics of the many-body energy spectrum are Poissonian. We moreover predict that a quench experiment starting from a charge-density wave state would show results similar to those of Schreiber et al. [Science 349, 842 (2015)SCIEAS0036-807510.1126/science.aaa7432].
Recent numerical and experimental works have revealed a disorder-free many-body localization (MBL) in an interacting system subjected to a linear potential, known as the Stark MBL. The conventional MBL, induced by disorder, has been widely studied by using quantum simulations based on superconducting circuits. Here, we consider the Stark MBL in two types of superconducting circuits, i.e., the one-dimensional array of superconducting qubits, and the circuit where nonlocal interactions between qubits are mediated by a resonator bus. We calculate the entanglement entropy and participate entropy of the highly excited eigenstates, and study the nonequilibrium properties of the Stark MBL. In particular, we observe an anomalous relaxation of the imbalance, dominated by the power-law decay ${t}^{\ensuremath{-}\ensuremath{\xi}}$. The exponent $\ensuremath{\xi}$ satisfies $\ensuremath{\xi}\ensuremath{\propto}|\ensuremath{\gamma}\ensuremath{-}{\ensuremath{\gamma}}_{c}{|}^{\ensuremath{\nu}}$ when $\ensuremath{\gamma}<{\ensuremath{\gamma}}_{c}$, and vanishes for $\ensuremath{\gamma}\ensuremath{\ge}{\ensuremath{\gamma}}_{c}$, which can be employed to estimate the ${\ensuremath{\gamma}}_{c}$. Our work indicates that superconducting circuits are a promising platform for investigating the critical properties of the Stark MBL transition.
In one-dimensional (1D) disorder-free interacting systems, a sufficiently strong linear potential can induce localization of the many-body eigenstates, a phenomenon dubbed as Stark many-body localization (MBL). In this paper, we investigate the fate of Stark MBL in 1D spinless fermions systems with long-range interactions, specifically focusing on the role of interaction strength. We obtain the Stark MBL phase diagrams by computing the mean gap ratio and many-body inverse participation ratio at half-filling. We show that, for short-range interactions, there is a qualitative symmetry between the limits of weak and strong interactions. However, this symmetry is absent in the case of long-range interactions, where the system is always Stark many-body localized at strong interactions, regardless of the linear potential strength. Furthermore, we study the dynamics of imbalance and entanglement with various initial states using time-dependent variational principle (TDVP) numerical methods. We reveal that the dynamical quantities display a strong dependence on the initial conditions, which suggests that the Hilbert-space fragmentation precludes thermalization. Our results demonstrate the robustness of Stark MBL even in the presence of long-range interactions and offer an avenue to explore MBL in disorder-free systems with long-range interactions.
The combination of strong disorder and interactions in closed quantum systems can lead to many-body localization (MBL). However, this quantum phase is not stable when the system is coupled to a thermal environment. We investigate how MBL is destroyed in systems that are weakly coupled to a dephasive Markovian environment by focusing on their entanglement dynamics. We numerically study the third R\'enyi negativity R3{R}_{3}R3​, a recently proposed entanglement proxy based on the negativity that captures the unbounded logarithmic growth in the closed case and that can be computed efficiently with tensor networks. We also show that the decay of R3{R}_{3}R3​ follows a stretched exponential law, similarly to the imbalance, with, however, a smaller stretching exponent.