Universal spectral correlations in interacting chaotic few-body quantum systems

TL;DR

This paper investigates universal spectral correlations in interacting chaotic quantum systems, revealing a transition in spectral form factors governed by a single parameter, with exact results and numerical validation in few- and many-body models.

Contribution

The study provides an exact analytical description of spectral form factor transitions in interacting quantum systems using random matrix theory, validated by numerical simulations and physical models.

Findings

Spectral correlations follow universal patterns described by a single scaling parameter.

Exact results for spectral form factors in large Hilbert spaces.

Numerical and physical system validations confirm theoretical predictions.

Abstract

The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in interacting chaotic few- and many-body systems, modeled by suitable random-matrix ensembles, and obtain exact results for large Hilbert space dimensions. The transition of the spectral form factor from the non-interacting to the strongly interacting case can be described as a simple combination of these two limiting cases, which we confirm by extensive numerical studies in few-body systems. This transition is universally governed by a single scaling parameter. Moreover, our approach accurately captures spectral correlations in actual physical system, which we demonstrate for coupled kicked rotors.