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 (3)

• Entanglement in a second order quantum phase transition
• Excited state quantum phase transitions in many-body systems
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections