Chaos in fermionic many-body systems and the metal-insulator transition

TL;DR

This paper demonstrates that finite fermionic many-body systems with mean field and few-body interactions typically exhibit chaotic spectral fluctuations similar to Wigner-Dyson statistics, linking chaos to the metal-insulator transition.

Contribution

It introduces a sparse random-matrix ensemble to model the metal-insulator transition and shows that generic fermionic systems are less sparse and thus chaotic.

Findings

Fermionic many-body systems display Wigner-Dyson spectral fluctuations.

A new sparse random-matrix ensemble (ScE) models the metal-insulator transition.

Generic fermionic systems are less sparse and exhibit chaos.

Abstract

We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix ensemble ScE that mimics that transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.