Trace formula for spin chains

TL;DR

This paper derives a trace formula linking quantum energy levels to classical dynamics in spin chains, extending semiclassical analysis to many-body systems with large spin, applicable to both continuous and driven cases.

Contribution

It introduces a trace formula for coupled spin j particles, connecting quantum spectra to classical trajectories in the large j limit, including time-dependent scenarios.

Findings

Derived a trace formula for spin chains in the large j limit.

Explained the omission of the Solari-Kochetov phase with proper Hamiltonian choice.

Applicable to both time-continuous and periodically driven spin systems.

Abstract

While detailed information about the semiclassics for single-particle systems is available, much less is known about the connection between quantum and classical dynamics for many-body systems. As an example, we focus on spin chains which are of considerable conceptual and practical importance. We derive a trace formula for coupled spin $j$ particles which relates the quantum energy levels to the classical dynamics. Our derivation is valid in the limit $j\rightarrow\infty$ with $j\hbar={\rm const.}$ and applies to time-continuous as well as to periodically driven dynamics. We provide a simple explanation why the Solari-Kochetov phase can be omitted if the correct classical Hamiltonian is chosen.