Quasi-Exactly Solvable Models Derived from the Quasi-Gaudin Algebra

Details Quasi-Exactly Solvable Models Derived from the Quasi-Gaudin Algebra Quasi-Exactly Solvable Models Derived from the Quasi-Gaudin Algebra

2011-08-23

arxiv.org/abs/1108.4507v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, no figures

Scientific paper

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.

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