The role of classical periodic orbits in quantum many-body systems

TL;DR

This paper explores how a duality relation can be used to analyze classical orbits in quantum many-body systems, overcoming exponential complexity issues in semiclassical analysis.

Contribution

It introduces a duality approach to extract classical orbits from quantum spectra in many-body systems, extending semiclassical methods beyond single-particle cases.

Findings

Successfully applied duality to the kicked spin chain example.

Analyzed spectral statistics of chaotic many-body systems.

Discussed limits of large semiclassical parameter and particle number.

Abstract

Semiclassical methods have been applied very successfully to describe the nontrivial transition from the quantum to the classical regime in $\textit{single}$-particle or at least $\textit{few}$-particle systems. Challenges on the way to an extension to $\textit{many}$-body systems result from the exponential proliferation of the number of classical orbits in chaotic systems and the exponential growth of the quantum Hilbert-space dimension with the particle number. To circumvent these problems, we apply here our recently developed duality relation. Considering the kicked spin chain as example for a many-body system, we show how the duality relation can be used to extract the classical orbits from the quantum spectrum. For coupled cat maps, we analyze the spectral statistics of chaotic many-body systems and discuss the double limit of large semiclassical parameter and large particle number.