In this talk I will present results obtained on fully-connected mean-field models of quantum spins with p-body ferromagnetic interactions and a transverse field, as a toy model for studying quantum annealing of disordered systems. For p=2 this corresponds to the quantum Curie-Weiss model which exhibits a second-order phase transition, while for p>2 the transition is first order. We provide a refined analytical description of both the static and dynamics properties of these models, allowing us to study the slow annealing from the pure transverse field to the pure ferromagnet (and vice versa) and discuss the effect of first-order phase transition and spinodals on the residual excitation energy, both on finite and exponentially divergent time-scales. We expect the general features that we found to be relevent for real disordered optimization problems.
Go to day