Crossing and anti-crossing of the Lipkin-Meshkov-Glick model for N = 4 spin system

Abstract

Energy level crossings are degeneracies of two or more energy levels which occur when two levels coincide due to the tuning of an external parameter. In this work, we observe the "motion" of the energy levels in terms of the applied external magnetic field and anisotropy. We demonstrate how the eigenenergies of the anisotropic Lipkin-Meshkov-Glick (LMG) model for the N = 4 spin system shift as a function of the aforementioned parameters. The resulting plots show multiple level crossings as the system becomes isotropic where the LMG model has degenerate ground states along the critical lines determined by the anisotropy parameter. This work has also verified that for the isotropic case, energy level crossings occur exactly at the critical points.