Marginal Anderson localization and many-body delocalization

Annu. Rev. Condens. Matter Phys.

Huse²

2015

Self Cite

2,413

2,415

We review some recent developments in the statistical mechanics of isolated quantum systems.We provide a brief introduction to quantum thermalization, paying particular attention to the 'Eigenstate Thermalization Hypothesis' (ETH), and the resulting 'single-eigenstate statistical mechanics'. We then focus on a class of systems which fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can locally remember forever information about their local initial conditions, and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL), and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveals dynamically-stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality where equilibrium ordering is forbidden.

Section: Localization Protected Topological Ordermentioning

confidence: 99%

“…Since general arguments [75,76] constrain ν ≥ 2/d, it appears that many-body localization can not occur in such systems. For a further discussion of these issues, see [74].…”

Section: Localization Protected Topological Ordermentioning

confidence: 99%

Many-Body Localization and Thermalization in Quantum Statistical Mechanics

Annu. Rev. Condens. Matter Phys.

Huse²

2015

Self Cite

2,413

2,415

“…We now imagine coupling the dot model (14) to a generic, ergodic bath. The bath-mediated interaction is taken to have the particle-number-conserving form…”

Section: 45mentioning

confidence: 99%

Mean-field theory of nearly many-body localized metals

Gopalakrishnan¹,

2014

Phys. Rev. B

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We develop a mean-field theory of the metallic phase near the many-body localization (MBL) transition, using the observation that a system near the MBL transition should become an increasingly slow heat bath for its constituent parts. As a first step, we consider the properties of a many-body localized system coupled to a generic ergodic bath whose characteristic dynamical timescales are much slower than those of the system. As we discuss, a wide range of experimentally relevant systems fall into this class; we argue that relaxation in these systems is dominated by collective many-particle rearrangements, and compute the associated timescales and spectral broadening. We then use the observation that the self-consistent environment of any region in a nearly localized metal can itself be modeled as a slowly fluctuating bath to outline a self-consistent mean-field description of the nearly localized metal and the localization transition. In the nearly localized regime, the spectra of local operators are highly inhomogeneous and the typical local spectral linewidth is narrow. The local spectral linewidth is proportional to the DC conductivity, which is small in the nearly localized regime. This typical linewidth and the DC conductivity go to zero as the localized phase is approached, with a scaling that we calculate, and which appears to be in good agreement with recent experimental results (Ref. 1).

“…In this supplement we estimate this interaction, first for ξ c < 1 and then for ξ c > 1. The calculation follows [16]. The two processes contributing to the effective interaction at lowest order in perturbation theory in weak G are shown in Fig.1.…”

mentioning

confidence: 99%

Many-body localization proximity effect

2015

Phys. Rev. B

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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 work 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 for two different types of 'weak' bath -baths which are close to an atomic limit, and baths which are close to a non-interacting limit. The existence of this 'many body localization proximity effect' indicates that many body localization is more robust than previously appreciated, and can not only survive coupling to a (weak) heat bath, but can even destroy the bath.Quantum localized systems violate many of the foundational assumptions of quantum statistical physics (such as the ergodic hypothesis), and present an exciting new frontier for research [1]. While localization was long believed to occur mainly in systems of non-interacting particles, the recent discovery of many body localization (MBL) [2][3][4][5] has ignited a blaze of interest in this field. It has been realized that quantum localized systems can display a cornucopia of exotic properties, including an emergent integrability [6][7][8], exotic quantum states of matter [9][10][11][12][13][14][15][16][17][18], and unexpected behavior in linear [19] and non-linear [20] response. These properties not only dramatically revise our understanding of quantum statistical physics, but also offer a new route to dissipationless quantum technologies. A summary of progress in this field can be found in the review article [21].Most works on MBL have focused on perfectly isolated quantum systems. Experimental systems, however, are always coupled (however weakly) to a thermalizing environment. The behavior of many body localized systems coupled to a thermalizing environment was first examined in [22][23][24], in the limit where back action on the bath was negligible and the bath could be treated as Markovian. In this limit, it was argued that an arbitrarily weak coupling to a thermodynamically large bath should restore ergodicity, thermalizing the system. These results suggested that perfect MBL would be unobservable in experiments, which would see instead only signatures of proximity to a localized phase. However, these works left open the question of whether different physics could result if the localization in the system were strong, and the bath were weak. Could many body localization then survive even after coupling to a heat bath?In this Letter, we show that when the system of interest is strongly localized, and the 'heat bath' is only weakly ergodic, then MBL in the system can not only survive coupling to the bath, but can e...