Exploration of the stability of many-body localization in d > 1

Potirniche, Ionut-Dragos and Banerjee, Sumilan and Altman, Ehud (2019) Exploration of the stability of many-body localization in d > 1. In: PHYSICAL REVIEW B, 99 (20).

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Abstract

Recent work by De Roeck et al. Phys. Rev. B 95, 155129 (2017)] has argued that many-body localization is unstable in two and higher dimensions due to a thermalization avalanche triggered by rare regions of weak disorder. To examine these arguments, we construct several models of a finite ergodic bubble coupled to an Anderson insulator of noninteracting fermions. We first describe the ergodic region using a Gaussian orthogonal ensemble random matrix and perform an exact diagonalization study of small systems. The results are in excellent agreement with a refined theory of the thermalization avalanche that includes transient finite-size effects, lending strong support to the avalanche scenario. We then explore the limit of large system sizes by modeling the ergodic region via a Hubbard model with all-to-all random hopping: the combined system, consisting of the bubble and the insulator, can be reduced to an effective Anderson impurity problem. We find that the spectral function of a local operator in the ergodic region changes dramatically when coupling to a large number of localized fermionic states; this occurs even when the localized sites are weakly coupled to the bubble. In principle, for a given size of the ergodic region, this may arrest the avalanche. However, this back-action effect is suppressed and the avalanche can be recovered if the ergodic bubble is large enough. Thus, the main effect of the back-action is to renormalize the critical bubble size.

Item Type:	Journal Article
Publication:	PHYSICAL REVIEW B
Publisher:	AMER PHYSICAL SOC
Additional Information:	copyright for this article belongs to PHYSICAL REVIEW B
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	24 Jun 2019 20:12
Last Modified:	24 Jun 2019 20:12
URI:	http://eprints.iisc.ac.in/id/eprint/63053

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