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Entropy 2016, 18(4), 122; doi:10.3390/e18040122

Many-Body-Localization Transition in the Strong Disorder Limit: Entanglement Entropy from the Statistics of Rare Extensive Resonances

1
Institut de Physique Théorique, Commissariat à l’Energie Atomique (CEA), 91191 Gif-sur-Yvette, France
2
Centre National de la Recherche Scientifique (CNRS), Institut de Physique (INP), Unité Mixte de Recherches (UMR) 3681, Avenue de la Terrasse, 91190 Gif-sur-Yvette, France
3
Université Paris Saclay, 91190 Saint-Aubin, France
Academic Editor: Jay Lawrence
Received: 25 January 2016 / Revised: 22 March 2016 / Accepted: 29 March 2016 / Published: 1 April 2016
(This article belongs to the Special Issue Quantum Information 2016)
View Full-Text   |   Download PDF [337 KB, uploaded 1 April 2016]

Abstract

The space of one-dimensional disordered interacting quantum models displaying a many-body localization (MBL) transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the localized phase and the Wigner–Dyson statistics of the delocalized phase. In this paper, we consider the strong disorder limit of the MBL transition, where the level statistics at the MBL critical point is close to the Poisson statistics. We analyze a one-dimensional quantum spin model, in order to determine the statistical properties of the rare extensive resonances that are needed to destabilize the MBL phase. At criticality, we find that the entanglement entropy can grow with an exponent 0 < α < 1 anywhere between the area law α = 0 and the volume law α = 1 , as a function of the resonances properties, while the entanglement spectrum follows the strong multifractality statistics. In the MBL phase near criticality, we obtain the simple value ν = 1 for the correlation length exponent. Independently of the strong disorder limit, we explain why, for the many-body localization transition concerning individual eigenstates, the correlation length exponent ν is not constrained by the usual Harris inequality ν 2 / d , so that there is no theoretical inconsistency with the best numerical measure ν = 0 . 8 ( 3 ) obtained by Luitz et al. (2015). View Full-Text
Keywords: many-body-localization; entanglement; random quantum spin chains many-body-localization; entanglement; random quantum spin chains
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Monthus, C. Many-Body-Localization Transition in the Strong Disorder Limit: Entanglement Entropy from the Statistics of Rare Extensive Resonances. Entropy 2016, 18, 122.

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