Quasi-Exactly Solvable Models Derived from the Quasi-Gaudin Algebra
arXiv:1108.4507 · doi:10.1088/1751-8113/44/48/482001
Abstract
The quasi-Gaudin algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation of the quasi-Gaudin algebra, we obtain a class of bosonic models which exhibit this curious property. These models have the notable feature that they do not preserve U(1) symmetry, which is typically associated to a non-conservation of particle number. An exact solution for the eigenvalues within the quasi-exactly solvable sector is obtained via the algebraic Bethe ansatz formalism.
9 pages, no figures
References in corpus (8)
- Matrix Product States: Symmetries and Two-Body Hamiltonians
- Separation of variables for integrable spin-boson models
- Integrable spin-boson models descending from rational six-vertex models
- Exact solution of the p+ip pairing Hamiltonian and a hierarchy of integrable models
- Exact solutions for a family of spin-boson systems
- New exact solutions of the standard pairing model for well-deformed nuclei
- Matter-wave squeezing and the generation of SU(1,1) and SU(2) coherent-states via Feshbach resonances
- Exactly solvable models and ultracold Fermi gases