  In two dimensions a vortex lattice can melt by quantum fluctuations into a
non-superfluid Quantum Vortex Liquid (QVL). To determine the melting
conditions, we compute the bare vortex hopping rate by exact diagonalization of
square clusters near half filling. Mapping our effective Hamiltonian to the
Boson Coloumb Liquid simulated in Phys. Rev. Lett. 73, 826 (1994), we expect a
QVL above a melting density of 0.0065 vortices per lattice site. We also
compute the Hall conductivity using adiabatic curvatures. As a function of
boson filling it reverses sign at half filling in a sharp transition
accompanied by a vanishing temperature scale. At half filling, each vortex
carries a spin half quantum number (`v-spin'), as a consequence of local non
commuting SU(2) symmetries. Implications of these results could be realized in
cold atoms, Josephson junction arrays and cuprate superconductors.
