Semiclassical Identification of Periodic Orbits in a Quantum Many-Body System

TL;DR

This paper advances semiclassical methods to identify periodic orbits in quantum many-body systems, specifically analyzing a kicked spin chain to understand the interplay of regular and chaotic dynamics.

Contribution

It introduces a novel approach leveraging a duality relation to make semiclassical analysis feasible for complex many-body quantum systems.

Findings

Identification of collective coherent motion in the spin chain

Evidence of mixed regular and chaotic dynamics

Application of duality relation to semiclassical analysis

Abstract

While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems feasible, which is nontrivial due to the exponential proliferation of orbits with increasing particle number. Employing a recently discovered duality relation, we focus on the collective, coherent motion that together with the also present incoherent one typically leads to a mixture of regular and chaotic dynamics. We investigate a kicked spin chain as an example of a presently experimentally and theoretically much studied class of systems.