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Journal Club for Condensed Matter Physics

Is the many body localization transition accessible to computation?

Published Nov 30, 2019• 0 citations
Publisher

Abstract

1. Quantum chaos challenges many-body localization Authors: J. Šuntajs, J. Bonča, T. Prosen, and L. Vidmar arXiv:1905.06345 2. Distinguishing localization from chaos: challenges in finite-size systems Authors: D. A. Abanin, J. H. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. A. Parameswaran, F. Pollmann, A. C. Potter, M. Serbyn, and R. Vasseur arXiv:1911.04501 3. […]

DOI
10.36471/jccm_november_2019_01

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  1. Quantum chaos challenges many-body localization Authors: J. Šuntajs, J. Bonča, T. Prosen, and L. Vidmar arXiv:1905.06345 2. Distinguishing localization from chaos: challenges in finite-size systems Authors: D. A. Abanin, J. H. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. A. Parameswaran, F. Pollmann, A. C. Potter, M. Serbyn, and R. Vasseur arXiv:1911.04501 3. […]
This article is a brief introduction to the rapidly evolving field of many‐body localization. Rather than giving an in‐depth review of the subject, our aspiration here is simply to introduce the problem and its general context, outlining a few directions where notable progress has been achieved in recent years. We hope that this will prepare the readers for the more specialized articles appearing in this dedicated Volume of Annalen der Physik, where these developments are discussed in more detail. image
Two of the most active areas in quantum many-particle dynamics involve systems with an unusually large number of conservation laws. Many-body-localized systems generalize ideas of Anderson localization by disorder to interacting systems. While localization still exists with interactions and inhibits thermalization, the interactions between conserved quantities lead to some dramatic differences from the Anderson case. Quantum integrable models such as the XXZ spin chain or Bose gas with delta-function interactions also have infinite sets of conservation laws, again leading to modifications of conventional thermalization. A practical way to treat the hydrodynamic evolution from local equilibrium to global equilibrium in such models is discussed. This paper expands upon a presentation at a discussion meeting of the Royal Society on 7 February 2017. The work described was carried out with a number of collaborators, including Jens Bardarson, Vir Bulchandani, Roni Ilan, Christoph Karrasch, Siddharth Parameswaran, Frank Pollmann and Romain Vasseur.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
Recent experiments in quantum simulators have provided evidence for the many-body localized (MBL) phase in one-dimensional (1D) and two-dimensional (2D) bosonic quantum matter. The theoretical study of such a bosonic MBL phase, however, is a daunting task due to the unbounded nature of its Hilbert space. In this work, we introduce a method to compute the long-time real-time evolution of 1D and 2D bosonic systems in an MBL phase at strong disorder and weak interactions. We focus on local dynamical indicators that are able to distinguish an MBL phase from an Anderson localized one. In particular, we consider the temporal fluctuations of local observables, the spatiotemporal behavior of two-time correlators and out-of-time-correlators. We show that these few-body observables can be computed with a computational effort that depends only polynomially on the system size but is independent of the target time, by extending a recently proposed numerical method [G. De Tomasi, F. Pollmann, and M. Heyl, Phys. Rev. B 99, 241114(R) (2019)] to mixed states and bosons. Our method also allows us to surrogate our numerical study with analytical considerations of the time-dependent behavior of the studied quantities.
What happens in an isolated quantum system when both disorder and interactions are present? Over the recent years, the picture of a non-thermalizing phase of matter, the many-localized phase, has emerged as a stable solution. We present a basic introduction to the topic of many-body localization, using the simple example of a quantum spin chain that allows us to illustrate several of the properties of this phase. We then briefly review the current experimental research efforts probing this physics. The largest part of this review is a selection of more specialized questions, some of which are currently under active investigation. We conclude by summarizing the connections between many-body localization and quantum simulations.