Exact solutions for the LMG model Hamiltonian based on the Bethe ansatz

Exact solutions for the Lipkin–Meshkov–Glick (LMG) model Hamiltonian are obtained by solving the Bethe ansatz equation (BAE) which is derived from the variation equation based on the Bethe ansatz. Unlike Pan and Draayer, we do not use bosonization and infinite-dimensional algebra techniques. Consequently there are no restrictions on parameters specifying strengths of the interactions included in the LMG Hamiltonian. Thus, for all the regimes of the interaction parameters, we get the exact solutions for the LMG Hamiltonian by numerically solving the BAEs and give the numerical behaviour of an order parameter 〈Jx2〉.