Entanglement entropy in the Lipkin-Meshkov-Glick model

Abstract

We analyze the entanglement entropy in the Lipkin-Meshkov-Glick model, which describes mutually interacting spin 1/2 embedded in a magnetic field. This entropy displays a singularity at the critical point that we study as a function of the interaction anisotropy, the magnetic field, and the system size. Results emerging from our analysis are surprisingly similar to those found for the one- dimensional $XY$ chain.