Asymptotic quantum many-body localization from thermal disorder
type: Item
instance of: scholarly article
title: Asymptotic quantum many-body localization from thermal disorder
zbMATH Open document ID: 1309.82010
author: W. De Roeck
author: François Huveneers
published in: Communications in Mathematical Physics
publication date: 2014-10-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1308.6263
review text: A quantum lattice system is considered akin to the Bose-Hubbard model. The many-body localization is investigated, that is induced by thermal fluctuations rather than by the disorder in the Hamiltonian. This is an important departure from current approaches to the delocalization-localization (or metal-insulator) transition, normally expected to occur with the growth of the disorder strength. Major rigorous results about the localized regime have been obtained in the context of non-interacting electrons in random lattices. The authors address a difficult problem of how many-body interactions modify the metal-insulator transition. There is a consensus that the latter transition occurs at least for short range interactions. However, there is no mathematical proof of many-body localization. All models considered so far have a disorder built-in in the Hamiltonian. Here the perspective changes and amounts to replacing that disorder by thermal fluctuations, due to the thermal Gibbs state. A characterization of localization is given in terms of the dynamics of energy fluctuations which is embodied by the Green-Kubo formula for the heat conductivity. The many body localization is understood as the vanishing of conductivity. The main result of the paper is a demonstration that the Green-Kubo conductivity in the considered model decays faster than any polynomial if the inverse temperature \(\beta \) as \(\beta \rightarrow 0\).
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 82B26
Mathematics Subject Classification ID: 81V70
Mathematics Subject Classification ID: 82B10
zbMATH DE Number: 6359803
zbMATH Keywords: quantum lattice system
zbMATH Keywords: many body localization
zbMATH Keywords: Green-Kubo conductivity
zbMATH Keywords: metal-insulator transition
zbMATH Keywords: localized phase
zbMATH Keywords: thermal disorder
zbMATH Keywords: eigenstate thermalization hypothesis (ETH)
zbMATH Keywords: perturbative diagonalization
zbMATH Keywords: resonant Hamiltonian
zbMATH Keywords: invariant subspaces
zbMATH Keywords: decay of correlations
zbMATH Keywords: polymer representations
zbMATH Keywords: cluster expansion
MaRDI profile type: Publication
OpenAlex ID: W3105363476
arXiv ID: 1308.6263
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DOI: 10.1007/S00220-014-2116-8
description: scientific article; zbMATH DE number 6359803