Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model

Abstract

We introduce a novel semiclassical approach to the Lipkin model. In this way the well-known phase transition arising at the critical value of the coupling is intuitively understood. New results -- showing for strong couplings the existence of a threshold energy which separates deformed from undeformed states as well as the divergence of the density of states at the threshold energy -- are explained straightforwardly and in quantitative terms by the appearance of a double well structure in a classical system corresponding to the Lipkin model. Previously unnoticed features of the eigenstates near the threshold energy are also predicted and found to hold.