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

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Lee, Yuan-Harng ; Links, Jon ; Zhang, Yao-Zhong (2011)
  • Related identifiers: doi: 10.1088/1751-8113/44/48/482001
  • Subject: Mathematical Physics | Nonlinear Sciences - Exactly Solvable and Integrable Systems | Condensed Matter - Statistical Mechanics | High Energy Physics - Theory
    arxiv: Nonlinear Sciences::Exactly Solvable and Integrable Systems

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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