平均场量子自旋系统的谱隙和低能谱

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2023-12-06 DOI:10.1017/fms.2023.111

Chokri Manai, Simone Warzel

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引用次数: 0

摘要

采用基于自旋相干态的半经典分析方法，建立了平均场自旋哈密顿量谱隙的分类和新的简单公式。对于间隙系统，我们提供了基于二阶近似半经典哈密顿量的低能谱的完整描述，从而证明了在这种情况下零温度下的涨落理论。我们还指出了二阶近似中由球面几何引起的位移。

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

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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来源期刊

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.