Notes on solvable models of many-body quantum chaos

TL;DR

This paper investigates a class of many-body quantum chaos models related to the Brownian SYK model, revealing universal behaviors and emergent symmetries that map quantum dynamics to classical stochastic processes, enabling analysis at finite N.

Contribution

It introduces a framework connecting quantum chaos models to classical stochastic processes, allowing finite N analysis and comparison with field theory, and explores operator growth and entanglement dynamics.

Findings

Universal behaviors emerge at large N

Quantum dynamics can be mapped to classical stochastic processes

Operator size growth and entanglement dynamics are characterized

Abstract

We study a class of many body chaotic models related to the Brownian Sachdev-Ye-Kitaev model. An emergent symmetry maps the quantum dynamics into a classical stochastic process. Thus we are able to study many dynamical properties at finite N on an arbitrary graph structure. A comprehensive study of operator size growth with or without spatial locality is presented. We will show universal behaviors emerge at large N limit, and compare them with field theory method. We also design simple stochastic processes as an intuitive way of thinking about many-body chaotic behaviors. Other properties including entanglement growth and other variants of this solvable models are discussed.