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

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.

Extended published version

References in corpus (7)

• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• On quantum mean-field models and their quantum annealing
• The Phase Diagram of the Quantum Curie-Weiss Model
• Central limit theorems for the large-spin asymptotics of quantum spins
• Semi-Classical Dynamics in Quantum Spin Systems
• Spectral Analysis of the Quantum Random Energy Model
• The large-spin asymptotics of the ferromagnetic XXZ chain