Phase space analysis of first-, second- and third-order quantum phase transitions in the Lipkin-Meshkov-Glick model

We present a phase-space study of first-, second-and third-order quantum phase transitions in the Lipkin-Meshkov-Glick model by means of the Husimi function. By analyzing the distribution of zeros of the ground state Husimi function we have characterized each phase and each type of quantum phase transition in this model. We show that Renyi-Wehrl entropies of the ground state Husimi function give a good description of quantum phase transitions. The study has been done using a numerical treatment and a variational approximation in terms of coherent states. Additionally, we have analyzed quantum phase transitions using the fidelity and fidelity susceptibility concepts.