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

被引：0
|
作者：
Manai, Chokri [1 ]
Warzel, Simone [1 ,2 ]
机构：
[1] TUM, Dept Math, Boltzmannstr 3, D-85748 Munich, Germany
[2] TUM, Dept Phys, James Franck Str 1, D-85748 Munich, Germany
来源：
FORUM OF MATHEMATICS SIGMA | 2023年 / 11卷
关键词：
81Q10; 81Q20; 81R30; BODY APPROXIMATION METHODS; SEMI-CLASSICAL LIMIT; SOLVABLE MODEL; VALIDITY; STATES; MECHANICS; DYNAMICS; DIAGRAM;
D O I：
10.1017/fms.2023.111
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A semiclassical analysis based on spin-coherent states is used to establish a classification and novel simple 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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页数：34
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