Many-body quantum chaos and emergence of Ginibre ensemble

TL;DR

This paper demonstrates that non-Hermitian Ginibre random matrix behavior naturally arises in spatially-extended many-body quantum chaotic systems, revealing a new universality class linked to the system's spatial structure.

Contribution

It establishes the emergence of Ginibre ensemble statistics in many-body quantum chaos, extending the understanding of universality classes beyond Hermitian matrices.

Findings

Ginibre spectral correlations emerge in quantum chaos systems

The spectral form factor matches Ginibre ensemble predictions in the large system limit

The phenomenon generalizes to non-translationally invariant models

Abstract

We show that non-Hermitian Ginibre random matrix behaviors emerge in spatially-extended many-body quantum chaotic systems in the space direction, just as Hermitian random matrix behaviors emerge in chaotic systems in the time direction. Starting with translational invariant models, which can be associated with dual transfer matrices with complex-valued spectra, we show that the linear ramp of the spectral form factor necessitates that the dual spectra have non-trivial correlations, which in fact fall under the universality class of the Ginibre ensemble, demonstrated by computing the level spacing distribution and the dissipative spectral form factor. As a result of this connection, the exact spectral form factor for the Ginibre ensemble can be used to universally describe the spectral form factor for translational invariant many-body quantum chaotic systems in the scaling limit where $t$ and $L$ are large, while the ratio between $L$ and $L_{\mathrm{Th}}$, the many-body Thouless length is fixed. With appropriate variations of Ginibre models, we analytically demonstrate that our claim generalizes to models without translational invariance as well. The emergence of the Ginibre ensemble is a genuine consequence of the strongly interacting and spatially extended nature of the quantum chaotic systems we consider, unlike the traditional emergence of Hermitian random matrix ensembles.