Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

Understand

The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin coherent states formalism.

• In the first step, a classical analysis allows one to distinguish between four distinct regions in the parameter space according to the nature of the singularities arising in the classical energy surface; these correspond to spectral critical points.
• The eigenfunctions are then analyzed more precisely in terms of the associated roots of the Majorana polynomial, leading to exact expressions for the density of states in the thermodynamic limit.
• Finite-size effects are also analyzed, leading in particular to logarithmic corrections near the singularities occuring in the spectrum.