Spectral statistics in spatially extended chaotic quantum many-body systems

TL;DR

This paper investigates spectral statistics in chaotic quantum many-body systems, revealing how the Thouless time depends on system dimension and size, with implications for understanding quantum chaos and thermalization.

Contribution

It provides an analytical and numerical analysis of spectral form factors in lattice Floquet models, highlighting the dimension-dependent behavior of the Thouless time in many-body systems.

Findings

Spectral form factor follows RMT at times beyond the Thouless time.

Thouless time is finite for dimensions greater than one, set by inter-site coupling.

In one dimension, the Thouless time diverges with system size, delaying RMT behavior.

Abstract

We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor $K(t)$ analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a many-body Thouless time, $t_{\rm Th}$. We obtain a striking dependence of $t_{\rm Th}$ on the spatial dimension $d$ and size of the system. For $d>1$, $t_{\rm Th}$ is finite in the thermodynamic limit and set by the inter-site coupling strength. By contrast, in one dimension $t_{\rm Th}$ diverges with system size, and for large systems there is a wide window in which spectral correlations are not of RMT form.