Localization on Certain Graphs with Strongly Correlated Disorder

Roy, S and Logan, DE (2020) Localization on Certain Graphs with Strongly Correlated Disorder. In: Physical Review Letters, 125 (25).

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Abstract

Many-body localization in interacting quantum systems can be cast as a disordered hopping problem on the underlying Fock-space graph. A crucial feature of the effective Fock-space disorder is that the Fock-space site energies are strongly correlated - maximally so for sites separated by a finite distance on the graph. Motivated by this, and to understand the effect of such correlations more fundamentally, we study Anderson localization on Cayley trees and random regular graphs, with maximally correlated disorder. Since such correlations suppress short distance fluctuations in the disorder potential, one might naively suppose they disfavor localization. We find however that there exists an Anderson transition, and indeed that localization is more robust in the sense that the critical disorder scales with graph connectivity K as K, in marked contrast to KlnK in the uncorrelated case. This scaling is argued to be intimately connected to the stability of many-body localization. Our analysis centers on an exact recursive formulation for the local propagators as well as a self-consistent mean-field theory; with results corroborated using exact diagonalization. © 2020 American Physical Society.

Item Type:	Journal Article
Publication:	Physical Review Letters
Publisher:	American Physical Society
Additional Information:	Copyright to this article belongs to American Physical Society
Keywords:	Algebra; Mean field theory, Anderson localization; Anderson transition; Correlated disorder; Exact diagonalization; Interacting quantum systems; Random regular graph; Recursive formulation; Self-consistent mean-field theories, Trees (mathematics)
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	18 Jan 2021 09:43
Last Modified:	18 Jan 2021 09:43
URI:	http://eprints.iisc.ac.in/id/eprint/67607

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