The Generalized Lipkin-Meshkov-Glick Model and the Modified Algebraic Bethe Ansatz

Abstract

We show that the Lipkin-Meshkov-Glick $2N$-fermion model is a particular case of one-spin Gaudin-type model in an external magnetic field corresponding to a limiting case of non-skew-symmetric elliptic $r$-matrix and to an external magnetic field directed along one axis. We propose an exactly-solvable generalization of the Lipkin-Meshkov-Glick fermion model based on the Gaudin-type model corresponding to the same $r$-matrix but arbitrary external magnetic field. This model coincides with the quantization of the classical Zhukovsky-Volterra gyrostat. We diagonalize the corresponding quantum Hamiltonian by means of the modified algebraic Bethe ansatz. We explicitly solve the corresponding Bethe-type equations for the case of small fermion number $N=1,2$.

References in corpus (5)

• Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
• The Lipkin-Meshkov-Glick model as a particular limit of the SU(1,1) Richardson-Gaudin integrable models
• Read-Green resonances in a topological superconductor coupled to a bath
• Strong-coupling emergence of dark states in XX central spin models
• Ground-state energy of a Richardson-Gaudin integrable BCS model