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Vortex quantum dynamics of two dimensional lattice bosons

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.