Quasi-Exactly Solvable Models Derived from the Quasi-Gaudin Algebra
  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. 
Yuan-Harng Lee, Jon Links, Yao-Zhong Zhang
nlin.SI cond-mat.stat-mech hep-th math-ph math.MP