Asymptotic quantum many-body localization from thermal disorder

TL;DR

This paper demonstrates that in a quantum lattice system similar to the Bose-Hubbard model, thermal fluctuations induce many-body localization, with conductivity decaying faster than any polynomial as temperature increases.

Contribution

It provides rigorous evidence that thermal fluctuations can cause many-body localization in quantum systems with infinite-dimensional on-site Hilbert spaces.

Findings

Green-Kubo conductivity decays faster than any polynomial in inverse temperature

Rigorous proof of vanishing conductivity as temperature increases

Approximate conductivity measures tend to zero faster than any polynomial

Abstract

We consider a quantum lattice system with infinite-dimensional on-site Hilbert space, very similar to the Bose-Hubbard model. We investigate many-body localization in this model, induced by thermal fluctuations rather than disorder in the Hamiltonian. We provide evidence that the Green-Kubo conductivity $\kappa(\beta)$, defined as the time-integrated current autocorrelation function, decays faster than any polynomial in the inverse temperature $\beta$ as $\beta \to 0$. More precisely, we define approximations $\kappa_{\tau}(\beta)$ to $\kappa(\beta)$ by integrating the current-current autocorrelation function up to a large but finite time $\tau$ and we rigorously show that $\beta^{-n}\kappa_{\beta^{-m}}(\beta)$ vanishes as $\beta \to 0$, for any $n,m \in \mathbb{N}$ such that $m-n$ is sufficiently large.