Unconventional quantum phase transition in the finite-size Lipkin-Meshkov-Glick model

Abstract

The Lipkin model of arbitrary particle number N is studied in terms of exact differential-operator representation of spin-operators from which we obtain the low-lying energy spectrum with the instanton method of quantum tunnelling. Our new observation is that the well-known quantum phase transition (QPT) can also occur in the finite-N model only if N is an odd number. We furthermore demonstrate a new type of QPT characterized by level-crossing which is induced by the geometric phase interference and is marvellously periodic with respect to the coupling parameter. Finally, the conventional QPT is understood intuitively from the tunnelling formulation in the thermodynamic limit. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.