Characterization of many-body mobility edges with random matrices

Xingbo Wei; Rubem Mondaini; Gao Xianlong

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arXiv · 2001.04105

Characterization of many-body mobility edges with random matrices

Xingbo Wei·Rubem Mondaini·Gao Xianlong

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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.

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Xingbo Wei, Rubem Mondaini, Gao Xianlong. 2020-01-13. Characterization of many-body mobility edges with random matrices. https://arxiv.org/abs/2001.04105

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