The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems

TL;DR

This paper uses semiclassical analysis to classify spectral gaps and describe low-energy spectra in mean-field quantum spin systems, providing formulas and insights into fluctuations and geometric effects.

Contribution

It introduces a semiclassical approach for spectral gap classification and low-energy spectrum description, including geometric shift considerations.

Findings

Spectral gap classification formulae derived

Low-energy spectra characterized by second-order semiclassical approximation

Identification of a geometric shift effect in the approximations

Abstract

A semiclassical analysis based on spin-coherent states is used to establish a classification and formulae for the spectral gap of mean-field spin Hamiltonians. For gapped systems we provide a full description of the low-energy spectra based on a second-order approximation to the semiclassical Hamiltonian hence justifying fluctuation theory at zero temperature for this case. We also point out a shift caused by the spherical geometry in these second-order approximations.