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arXiv · 2302.00465

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

Chokri Manai·Simone Warzel
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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.

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Chokri Manai, Simone Warzel. 2023-02-01. The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems. https://doi.org/10.1017/fms.2023.111

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