Semi-classical Analysis of Spin Systems near Critical Energies

Abstract

The spectral properties of $su(2)$ Hamiltonians are studied for energies near the critical classical energy ${\epsilon }_c$ for which the corresponding classical dynamics presents hyperbolic points (HP). A general method leading to an algebraic relation for eigenvalues in the vicinity of ${\epsilon }_c$ is obtained in the thermodynamic limit, when the semi-classical parameter $n^{-1}=(2s{)}^{-1}$ 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 ${\epsilon }_c$, are also computed and shown to be in agreement with the numerical results.

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References in corpus (7)

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Cited by in corpus (7)

• Excited-state quantum phase transitions
• Quantum quench influenced by an excited-state phase transition
• On quantum mean-field models and their quantum annealing
• Integrable quantum dynamics of open collective spin models
• Excited-state quantum phase transitions and periodic dynamics
• The Lipkin-Meshkov-Glick model with Markovian dissipation -- A description of a collective spin on a metallic surface
• Wehrl entropy production rate across a dynamical quantum phase transition