Quantum phases of vortices in rotating Bose-Einstein condensates

We investigate the ground states of weakly, interacting bosons in a rotating trap as a function of the number of bosons, N, and the average number of vortices, N-v. We identify the filling fraction nu = N/N-v as the parameter controlling the nature of these states. We present results indicating that, as a function of nu, there is a zero temperature phase transition between a triangular vortex lattice phase, and strongly correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states.