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

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.