Quantum Phase Transition in Finite-Size Lipkin-Meshkov-Glick Model

TL;DR

This paper investigates quantum phase transitions in the finite-size Lipkin-Meshkov-Glick model, revealing that odd particle numbers exhibit unique phase transition behaviors due to level-crossing and geometric phase effects.

Contribution

It demonstrates that quantum phase transitions can occur in finite N models only for odd N and introduces a new type of transition driven by geometric phase interference.

Findings

Quantum phase transition occurs only for odd N in finite models.

A new transition type characterized by level-crossing and geometric phase interference.

Conventional transition understood via tunneling in the thermodynamic limit.

Abstract

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 tunneling. Our new observation is that the well known quantum phase transition can also occur in the finite-N model only if N is an odd-number. We furthermore demonstrate a new type of quantum phase transition characterized by level-crossing which is induced by the geometric phase interference and is marvelously periodic with respect to the coupling parameter. Finally the conventional quantum phase transition is understood intuitively from the tunneling formulation in the thermodynamic limit.