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

Chokri Manai, Simone Warzel

Published 2023-02-01Version 1

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.