Semiclassical mechanics of a non-integrable spin cluster

TL;DR

This paper investigates the classical-quantum correspondence in a three-spin system with anisotropic exchange, revealing how classical periodic orbits influence quantum density of states and energy level structures.

Contribution

It introduces a detailed analysis of classical-quantum correspondence in a non-integrable spin cluster, highlighting topology changes and spectral features using semiclassical methods.

Findings

Oscillating terms in quantum density of states linked to classical periodic orbits

Signs of topology changes in energy surfaces as energy varies

Hierarchy of quantum energy levels explained by EKB quantization and tunneling

Abstract

We study detailed classical-quantum correspondence for a cluster system of three spins with single-axis anisotropic exchange coupling. With autoregressive spectral estimation, we find oscillating terms in the quantum density of states caused by classical periodic orbits: in the slowly varying part of the density of states we see signs of nontrivial topology changes happening to the energy surface as the energy is varied. Also, we can explain the hierarchy of quantum energy levels near the ferromagnetic and antiferromagnetic states with EKB quantization to explain large structures and tunneling to explain small structures.