Instability of localization in translation-invariant systems
Abstract
The phenomenon of localization is usually accompanied with the presence of quenched disorder. To what extent disorder is necessary for localization is a well-known open problem. In this paper, we prove the instability of localization in translation-invariant systems. For any translation-invariant local Hamiltonian exhibiting either Anderson or many-body localization, an arbitrarily small translation-invariant random local perturbation almost surely leads to the following manifestations of delocalization: (i) Transport: For any (inhomogeneous) initial state, the spatial distribution of energy or any other local conserved quantity becomes uniform at late times. (ii) Scrambling: The out-of-time-ordered correlator of any traceless local operators decays to zero at late times. (iii) Thermalization: Random product states locally thermalize to the infinite temperature state with overwhelming probability.
Keywords
Cite
@article{arxiv.1907.13392,
title = {Instability of localization in translation-invariant systems},
author = {Yichen Huang and Aram W. Harrow},
journal= {arXiv preprint arXiv:1907.13392},
year = {2020}
}
Comments
v2 contains new results on the thermalization of random product states and a new author