We examine what happens when a strongly many-body localized system is coupled to a weak heat bath, with both system and bath containing similar numbers of degrees of freedom. Previous investigations of localized systems coupled to baths operated in regimes where the back action of the system on the bath is negligible and concluded that the bath generically thermalizes the system. In this paper we show that when the system is strongly localized and the bath is only weakly ergodic, the system can instead localize the bath. We demonstrate this both in the limit of weak coupling between system and bath and in the limit of strong coupling and also for two different types of ``weak'' bath---baths which are close to an atomic limit and baths which are close to a noninteracting limit. The existence of this ``many-body localization proximity effect'' indicates that many-body localization is more robust than previously appreciated, and it can not only survive coupling to a (weak) heat bath but can even destroy the bath.
We examine what happens when a strongly many-body localized system is coupled to a weak heat bath, with both system and bath containing similar numbers of degrees of freedom. Previous investigations of localized systems coupled to baths operated in regimes where the back action of the system on the bath is negligible and concluded that the bath generically thermalizes the system. In this paper we show that when the system is strongly localized and the bath is only weakly ergodic, the system can instead localize the bath. We demonstrate this both in the limit of weak coupling between system and bath and in the limit of strong coupling and also for two different types of weak'' bath---baths which are close to an atomic limit and baths which are close to a noninteracting limit. The existence of this many-body localization proximity effect'' indicates that many-body localization is more robust than previously appreciated, and it can not only survive coupling to a (weak) heat bath but can even destroy the bath.
We consider what happens when a many body localized system is coupled to a heat bath. Unlike previous works, we do not restrict ourselves to the limit where the bath is large and effectively Markovian, nor to the limit where back action on the bath is negligible. We identify limits where the effect of the bath can be captured by classical noise, and limits where it cannot. We also identify limits in which the bath delocalizes the system, as well as limits in which the system localizes the bath. Using general arguments and dimensional analysis, we constrain the overall phase diagram of the coupled system and bath. Our analysis incorporates all the previously discussed regimes, and also uncovers a new intrinsically quantum regime that has not hitherto been discussed. We discuss baths that are themselves near a localization transition, or are strongly disordered but protected against localization by symmetry or topology. We also discuss situations where the system and bath have different dimensionality (the case of ‘boundary MBL’ and ‘boundary baths’). image
In the presence of strong disorder and weak interactions, closed quantum systems can enter a many-body localized phase wherein the system does not conduct heat or charge, does not equilibrate even for arbitrarily long times, and robustly violates quantum statistical mechanics. While this is well established in closed quantum systems, the interplay of such systems with delocalized degrees of freedom is much less understood. Here, the authors consider a model for which, in the noninteracting limit, some degrees of freedom are localized while others remain delocalized. Such a system can be viewed as a model for a many-body localized system brought into contact with a small bath of a comparable number of degrees of freedom. The authors numerically and analytically study the effect of interactions on this system and find that in certain parameter regimes, results are consistent with interaction-induced localization of the entire system.
We study many-body-localized (MBL) systems that are weakly coupled to thermalizing environments, focusing on the spectral functions of local operators. These spectral functions carry signatures of localization even away from the limit of perfectly isolated systems. We find that, in the limit of vanishing coupling to a bath, MBL systems come in two varieties, with either discrete or continuous local spectra. Both varieties of MBL systems exhibit a ``soft gap'' at zero frequency in the spatially averaged spectral functions of local operators, which serves as a diagnostic for localization. We estimate the degree to which coupling to a bath broadens these spectral features, and we find that some characteristics of incipient localization survive as long as the system-bath coupling is much weaker than the characteristic energy scales of the system. We discuss the crossover to localization that occurs as the coupling to the external bath is tuned to zero. Since perfect isolation is impossible, we expect the ideas discussed in this paper to be relevant for experiments on many-body localization.
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 have left no doubt about 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 small quantum bath of adjustable size that is collisionally coupled to the dirty component. Our experiments provide evidence that MBL is remarkably stable in 2D and can even survive in the presence of a small bath for our observed long timescales. A too large bath, however, ultimately leads to the destruction of MBL.
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.
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.