Density correlations and transport in models of many-body localization

TL;DR

This paper reviews recent theoretical advances in understanding many-body localization, focusing on density correlations and transport, highlighting the ergodic transition, and discussing models like spinless fermions and Hubbard systems.

Contribution

It provides a comprehensive overview of the dynamical density correlations and transport in MBL, including new insights into the absence of full MBL in certain models.

Findings

Density correlations and transport are closely related in MBL.

Experimental findings are consistent with the theoretical ergodic-to-nonergodic transition.

Evidence suggests the absence of full MBL in the 1D Hubbard model.

Abstract

We present a review of recent theoretical results concerning the many-body localization (MBL) phenomenon, with the emphasis on dynamical density correlations and transport quantities. They are shown to be closely related, providing a comprehensive description of the ergodic-to-nonergodic transition, consistent with experimental findings. While the focus is set mostly on the one-dimensional model of interacting spinless fermions, we also present evidence for the absence of full MBL in the one-dimensional Hubbard model and for the density-wave decay induced by the inter-chain coupling.