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arXiv:2004.13072 · Physical review. B./Physical review. B

Entanglement dynamics of a many-body localized system coupled to a bath

Elisabeth Wybo, Michael Knap, Frank Pollmann

Published Aug 7, 2020• 42 citations
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Abstract

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 ${R}_{3}$, 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 ${R}_{3}$ follows a stretched exponential law, similarly to the imbalance, with, however, a smaller stretching exponent.

DOI
10.1103/physrevb.102.064304

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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.
An interacting system subjected to a strong linear potential can host a many‐body localized (MBL) phase when being slightly perturbed. This so‐called Wannier–Stark or “tilted‐field” MBL phase inherits many properties from the well‐investigated disordered MBL phase, and provides an alternative route to experimentally engineer interacting localized systems without quenched disorder. Herein, the dynamics of entanglement in a Wannier–Stark MBL system coupled to a dephasing environment is investigated. As an accessible entanglement proxy, the third Rényi negativity is used, which reduces to the third Rényi entropy in case the system is isolated from the environment. This measure captures the characteristic logarithmic growth of interacting localized phases in the intermediate‐time regime, where the effects of the coupling to the environment are not yet dominating the dynamics. Thus, it forms a tool to distinguish Wannier–Stark MBL from noninteracting Wannier–Stark localization up to intermediate time‐scales, and to quantify quantum correlations in mixed‐state dynamics.
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. Our numerical results indicate that in most cases, the system retains its localization properties despite the coupling to the finite environment, albeit to a reduced extent. However, in cases where the system and environment is strongly coupled in the ladder configuration, the eventual localization properties are highly dependent on the initial state, and could lead to either thermalization or localization.
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.
Many-body localization (MBL) is an example of a dynamical phase of matter that avoids thermalization. While the MBL phase is robust to weak local perturbations, the fate of an MBL system coupled to a thermalizing quantum system that represents a ``heat bath'' is an open question that is actively investigated theoretically and experimentally. In this work, we consider the stability of an Anderson insulator with a finite density of particles interacting with a single mobile impurity---a small quantum bath. We give perturbative arguments that support the stability of localization in the strong interaction regime. Large-scale tensor network simulations of dynamics are employed to corroborate the presence of the localized phase and give quantitative predictions in the thermodynamic limit. We develop a phenomenological description of the dynamics in the strong interaction regime, and we demonstrate that the impurity effectively turns the Anderson insulator into an MBL phase, giving rise to nontrivial entanglement dynamics well captured by our phenomenology.
Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is only experienced by one of the components. The second non-disordered ''clean'' component plays the role of a bath of adjustable size that is collisionally coupled to the ''dirty'' component. Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component. For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced. Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling and intercomponent interactions. They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.
Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL).Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems.However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions.Here we address this question experimentally using a largescale quantum simulator of ultracold bosons in a two-dimensional optical lattice.We prepare two-component mixtures of varying relative population and implement a disorder potential which is experienced only by one of the components.The second nondisordered "clean" component plays the role of a bath of adjustable size that is collisionally coupled to the "dirty" component.Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component.For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced.Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling, and intercomponent interactions.They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.