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arXiv:2012.13722 · Physical review. B./Physical review. B

Stark many-body localization: Evidence for Hilbert-space shattering

Elmer V. H. Doggen, I. V. Gornyi, Dmitry G. Polyakov

Published Mar 4, 2021• 60 citations
arXivHTMLPDF

Abstract

The ergodic hypothesis lies at the heart of classical statistical physics. A crucial question, therefore, is how this idea translates into the quantum world. Many-body localization -- the analog of Anderson localization to the many-body case -- has emerged as a key example of nonergodicity. Here, the authors analyze a disorder-free Heisenberg spin chain under the influence of a constant field gradient (Stark many-body localization). Surprisingly, they find that nonergodicity results, even for a vanishingly small gradient.

DOI
10.1103/physrevb.103.l100202

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The ergodic hypothesis lies at the heart of classical statistical physics. A crucial question, therefore, is how this idea translates into the quantum world. Many-body localization -- the analog of Anderson localization to the many-body case -- has emerged as a key example of nonergodicity. Here, the authors analyze a disorder-free Heisenberg spin chain under the influence of a constant field gradient (Stark many-body localization). Surprisingly, they find that nonergodicity results, even for a vanishingly small gradient.
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We introduce an analytic approach to many-body localization (MBL) in random spin chains. We consider MBL within a first quantized framework where it becomes a localization phenomenon in the high-dimensional lattice defined by the Hilbert space of the clean system. Designed in analogy with the field-theory description of single particle localization, our approach describes wave package propagation on that lattice after a disorder average has been performed and the system is controlled by only a few universal parameters. We discuss the stability of an ergodic weak disorder and a localized strong disorder phase, respectively, and demonstrate that the latter is protected by mechanisms which put MBL outside the universality class of Anderson localization.
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