Semiclassical analysis of spin systems near critical energies

2008/06/19 by Pedro Ribeiro, Thierry Paul · 1 citation
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Quantum chaos and dynamical systems #Quantum many-body systems #quant-ph

paper · pdf · doi:10.1103/physreva.79.032107

3 figures

arxiv created 2008/06/19 · openalex publication_date 2009/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spectral properties of su(2) Hamiltonians are studied for energies near the critical classical energy \ensuremathε_c for which the corresponding classical dynamics presents hyperbolic points. A general method leading to an algebraic relation for eigenvalues in the vicinity of \ensuremathε_c is obtained in the thermodynamic limit, when the semiclassical parameter n^\ensuremath-1=(2s)^\ensuremath-1 goes to zero (where s is the total spin of the system). Two applications of this method are given and compared with numerics. Matrix elements of observables, computed between states with energy near \ensuremathε_c, are also computed and shown to be in agreement with the numerical results.

Citations

• Validity of many-body approximation methods for a solvable model
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Bohr-Sommerfeld Quantization of Spin Hamiltonians
• Thermodynamical Limit of the Lipkin-Meshkov-Glick Model

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