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Quantum Monte Carlo studies of hard-core bosons with ring exchange



As a way of introducing a microscopic term that competes with the  superfluid (SF) phase in a model of hard-core bosons hopping on a square  lattice, a type of four-site ring-exchange was studied by Sandvik and
collaborators. Quantum Monte Carlo simulations revealed a number of  interesting features in this model, not least of which is the emergence  of a valence-bond solid (VBS) phase upon destruction of the superfluid.
Initial data appeared to indicate that the VBS phase commences via a  continuous quantum phase transition, a result that is unusual and  extremely controversial, since one typically expects such phase  transitions to be first-order. After nearly four years of intensive  computational work, the data for this phase transition still awaits a  perspicuous explanation. In this talk I will present the latest  numerical work on this and the extended family of ring-exchange models,  focusing not only on attempts to interpret the SF-VBS phase transition  (eg. in terms of the recent theory of deconfined quantum criticality),  but on other peculiar features of the phase diagrams.