The Lipkin-Meshkov-Glick model as a particular limit of the SU(1,1) Richardson-Gaudin integrable models

Understand

The Lipkin-Meshkov-Glick (LMG) model has a Schwinger boson realization in terms of a two-level boson pairing Hamiltonian.

• Through this realization, it has been shown that the LMG model is a particular case of the SU (1, 1) Richardson-Gaudin (RG) integrable models.
• We exploit the exact solvability of the model tostudy the behavior of the spectral parameters (pairons) that completely determine the wave function in the different phases, and across the phase transitions.
• Based on the relation between the Richardson equations and the Lam\'e differential equations we develop a method to obtain numerically the pairons.