• Open Access

Many-Body Localization with Long-Range Interactions

Rahul M. Nandkishore and S. L. Sondhi
Phys. Rev. X 7, 041021 – Published 25 October 2017

Abstract

Many-body localization (MBL) has emerged as a powerful paradigm for understanding nonequilibrium quantum dynamics. Folklore based on perturbative arguments holds that MBL arises only in systems with short-range interactions. Here, we advance nonperturbative arguments indicating that MBL can arise in systems with long-range (Coulomb) interactions, through a mechanism we dub “order enabled localization.” In particular, we show using bosonization that MBL can arise in one-dimensional systems with r interactions, a problem that exhibits charge confinement. We also argue that (through the Anderson-Higgs mechanism) MBL can arise in two-dimensional systems with logr interactions, and speculate that our arguments may even extend to three-dimensional systems with 1/r interactions. Our arguments are asymptotic (i.e., valid up to rare region corrections), yet they open the door to investigation of MBL physics in a wide array of long-range interacting systems where such physics was previously believed not to arise.

  • Received 2 June 2017

DOI:https://doi.org/10.1103/PhysRevX.7.041021

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Rahul M. Nandkishore1 and S. L. Sondhi2

  • 1Department of Physics and Center for Theory of Quantum Matter, University of Colorado at Boulder, Boulder, Colorado 80309, USA
  • 2Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

Popular Summary

Many-body localization (MBL) is a phenomenon whereby well-isolated quantum systems fail to reach thermal equilibrium even after an infinite amount of time. This is of interest for both conceptual reasons (it can stabilize entirely new quantum states of matter) and practical reasons (it can preserve quantum coherence at high temperatures). In the current theoretical understanding, MBL can occur when the physical degrees of freedom of a system interact only over short distances in space. However, physical systems frequently have long-range interactions, such as the attractive or repulsive force felt between electric charges. Previous theoretical attempts to establish MBL in systems with long-range interactions have failed, leading to a consensus that the two are incompatible. In this work, we theoretically demonstrate that, contrary to widespread belief, MBL is compatible with long-range interactions.

Our work makes use of nonperturbative methods for treating the interaction and is thus not limited by the breakdown of perturbation theory that has plagued previous attempts. Additionally, we use concepts drawn from gauge theory, such as confinement and the Anderson-Higgs mechanism, to provide powerful insights into the problem. We are able to show that MBL can arise in systems with long-range interactions in one, two, and perhaps even three spatial dimensions, at least when the interactions obey Gauss’s law (the fundamental law that is obeyed by electric and gravitational forces).

Our work opens the door to future investigations of MBL and related nonequilibrium quantum phenomena in systems with long-range interactions.

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Vol. 7, Iss. 4 — October - December 2017

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