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 governed by a single parameter, supported by analytical, numerical, and realistic system studies.

Contribution

It provides an exact analytical description of spectral form factor transitions in interacting quantum systems, extending to realistic models and small coupling regimes.

Findings

Universal transition from non-interacting to strongly interacting regimes

Exact spectral form factor for large Hilbert space

Validation through numerical and realistic system analysis

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 and its moments in interacting chaotic few- and many-body systems, modeled by suitable random-matrix ensembles. We obtain the spectral form factor exactly for large Hilbert space dimension. Extrapolating those results to finite Hilbert space dimension we find a universal transition from the non-interacting to the strongly interacting case, which can be described as a simple combination of these two limits. This transition is governed by a single scaling parameter. In the bipartite case we derive similar results also for all moments of the spectral form factor. We confirm our results by extensive numerical studies and demonstrate that they apply to more realistic systems given by a pair of quantized kicked rotors as well. Ultimately we complement our analysis by a perturbative approach covering the small coupling regime.