Bohr-Sommerfeld Quantization of Spin Hamiltonians

2003/04/05 by Anupam Garg, Michael Stone · 3 citations
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.92.010401

Revtex 4, no figures, 1 table

arxiv created 2003/04/05 · openalex publication_date 2004/01/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Bohr-Sommerfeld rule for a spin system is obtained, including the first quantum corrections. The rule applies to both integer and half-integer spin. It is tested for various models, in particular, the Lipkin-Meshkov-Glick model, and found to agree very well with exact results.

Citations

• Validity of many-body approximation methods for a solvable model
• Rotational energy surfaces and high-J eigenvalue structure of polyatomic molecules
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model

Cited by

• Semiclassical analysis of spin systems near critical energies
• Semiclassical quantization of anN-particle Bose-Hubbard model
• Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model