On quantum mean-field models and their quantum annealing

Abstract

This paper deals with fully connected mean-field models of quantum spins withp-body ferromagnetic interactions and a transverse field. Forp = 2 this corresponds to the quantum Curie–Weiss model (a special case of theLipkin–Meshkov–Glick model) which exhibits a second-order phase transition, while forp > 2 the transition is first order. We provide a refined analytical description both of the staticand of the dynamic properties of these models. In particular we obtain analytically theexponential rate of decay of the gap at the first-order transition. We also study the slowannealing from the pure transverse field to the pure ferromagnet (and vice versa) anddiscuss the effect of the first-order transition and of the spinodal limit of metastabilityon the residual excitation energy, both for finite and exponentially divergentannealing times. In the quantum computation perspective this quantity wouldassess the efficiency of the quantum adiabatic procedure as an approximationalgorithm.