Exact solutions for a family of spin-boson systems

Abstract

We obtain the exact solutions for a family of spin-boson systems. This is achieved through application of the representation theory for polynomial deformations of the $su(2)$ Lie algebra. We demonstrate that the family of Hamiltonians includes, as special cases, known physical models which are the two-site Bose-Hubbard model, the Lipkin-Meshkov-Glick model, the molecular asymmetric rigid rotor, the Tavis-Cummings model, and a two-mode generalisation of the Tavis-Cummings model.

LaTex 15 pages. To appear in Nonlinearity

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• Polynomial algebras and exact solutions of general quantum non-linear optical models I: Two-mode boson systems
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