Trace formula for spin chains

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.