Boundary Chaos: Spectral Form Factor

TL;DR

This paper investigates spectral correlations in a minimal model of quantum chaos with boundary interactions, showing that spectral form factors align with random matrix theory predictions, especially under resonance conditions, with results supported by both large Hilbert space and small dimension numerics.

Contribution

It introduces a boundary chaos model and provides exact calculations of spectral form factors, revealing their alignment with random matrix theory and the impact of resonance conditions.

Findings

Spectral form factor matches random matrix theory predictions.

Resonance conditions cause a drastic enhancement of spectral correlations.

Numerical results at small Hilbert space dimensions qualitatively agree with semiclassical analysis.

Abstract

Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed \textit{boundary chaos}, in terms of the spectral form factor and its fluctuations. We exactly calculate the latter in the limit of large local Hilbert space dimension $q$ for different classes of random boundary interactions and find it to coincide with random matrix theory, possibly after a non-zero Thouless time. The latter effect is due to a drastic enhancement of the spectral form factor, when integer time and system size fulfill a resonance condition. We compare our semiclassical (large $q$) results with numerics at small local Hilbert space dimension ($q=2,3$) and observe qualitatively similar features as in the semiclassical regime.