Abstract: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.