Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces

TL;DR

This paper investigates how quantum chaos emerges in spin systems with highly degenerate spectra, revealing a universal crossover to ergodicity influenced by system size and perturbation strength.

Contribution

It demonstrates that quantum chaos can appear in finite systems with degenerate spectra and characterizes the universal crossover to ergodicity in such models.

Findings

Quantum chaos can emerge in finite degenerate systems with small perturbations.

The onset of ergodicity occurs at perturbation strengths decreasing polynomially with system size.

Indicators like level spacing and entanglement reveal the crossover behavior.

Abstract

We show that in systems with highly degenerate energy spectra, such as the 2D transverse-field Ising model (2DTFIM) in the strong-field limit, quantum chaos can emerge in finite systems for arbitrary small perturbations. In this regime, the presence of extensive quasiconserved quantities can prevent finite systems from becoming ergodic. We study the ensuing crossover to ergodicity in a family of models that includes the 2DTFIM, in which the onset of ergodic behavior exhibits universality and occurs for perturbation strengths that decrease polynomially with increasing system size. We discuss the behaviors of quantum chaos indicators, such as level spacing statistics and bipartite entanglement, and of the fidelity susceptibilities and spectral functions across the crossover.