Semiclassical roots of universality in many-body quantum chaos

TL;DR

This paper explores how semiclassical methods reveal the universal features of quantum chaos in many-body systems, linking classical chaos to quantum behavior through a unified theoretical framework.

Contribution

It introduces a semiclassical many-body theory that extends single-particle techniques to account for genuine many-body quantum interference and universality.

Findings

Unified framework for single-particle and many-body quantum chaos

Classical orbit structures underpin quantum universality

Application to spectral density and out-of-time-order correlators

Abstract

Quantum chaos of many-body systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between classically chaotic dynamics and corresponding universal features at the quantum level. Recently, single-particle techniques dealing with ergodic wave interference in the usual semiclassical limit $\hbar \rightarrow 0$ have begun to be transformed into the field theoretical domain of N-particle systems in the analogous semiclassical limit $\hbar_{eff} = 1/N \rightarrow 0$, thereby accounting for genuine many-body quantum interference. This semiclassical many-body theory provides a unified framework for understanding random-matrix correlations of both single-particle and many-body quantum chaotic systems. Certain braided bundles of classical orbits, and of mean field modes, govern interference, respectively, and provide the key to the foundation of universality. Case studies presented include a many-body version of Gutzwiller's trace formula for the spectral density and out-of-time-order correlators along with brief remarks on where further progress may be forthcoming.