Emergence of many-body quantum chaos via spontaneous breaking of unitarity

TL;DR

This paper proposes that many-body quantum chaos arises from spontaneous breaking of unitarity, with interactions inducing a mass in the spectral form factor that influences level statistics and chaos indicators.

Contribution

It introduces a field theory framework showing how interactions cause a mass in the spectral form factor, leading to a transition from Poisson to random matrix statistics in many-body systems.

Findings

Interaction induces a finite mass in the spectral form factor.

Mass suppresses exponential ramp in the spectral form factor.

Transition from Poisson to random matrix level statistics occurs due to interactions.

Abstract

It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as $K(\eta,t)=\langle|{\rm Tr}\, \exp(-\eta H + itH)|^2\rangle$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the "unitary" $\eta=0$ case is different from the $\eta \to 0^{\pm}$ limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp in the SFF, which is responsible for the fast emergence of Poisson statistics in the non-interacting case, and gives rise to a non-trivial random matrix structure of many-body levels. The interaction-induced mass in the SFF shares similarities with the dephasing rate in the theory of weak localization and the Lyapunov exponent of the out-of-time-ordered correlators.