Characterization of many-body mobility edges with random matrices

TL;DR

This paper explores the existence of many-body mobility edges in one-dimensional quantum systems by using a novel random matrix approach, demonstrating their persistence in the large system limit and linking them to spectral statistics.

Contribution

It introduces a combined random matrix model with tunable distributions to study many-body mobility edges and confirms their existence in specific quantum systems.

Findings

Mobility edges can exist in large matrix limits depending on element distributions.

The transition from chaos to localization is characterized by spectral statistics.

Results connect mobility edges with level repulsion phenomena.

Abstract

Whether the many-body mobility edges can exist in a one-dimensional interacting quantum system is a controversial problem, mainly hampered by the limited system sizes amenable to numerical simulations. We investigate the transition from chaos to localization by constructing a combined random matrix, which has two extremes, one of Gaussian orthogonal ensemble and the other of Poisson statistics, drawn from different distributions. We find that by fixing a scaling parameter, the mobility edges can exist while increasing the matrix dimension $D\rightarrow\infty$, depending on the distribution of matrix elements of the diagonal uncorrelated matrix. By applying those results to a specific one-dimensional isolated quantum system of random diagonal elements, we confirm the existence of a many-body mobility edge, connecting it with results on the onset of level repulsion extracted from ensembles of mixed random matrices.