Vortices of Lattice Bosons Acquire Spin and Fermi Statistics

Lattice bosons a respond differently to a magnetic field, or a rotation, than continuum bosons, e.g. their Hall conductivity is not a linear function of their density. Such effects are mostly pronounced for hard-core bosons at half filling. For a periodic lattice on a torus threaded by fluxes, we can explicitly construct a conserved SU(2) `vortex spin' algebra. For odd total vorticity, even-fold spectral degeneracies are discovered on every lattice site. In particular, {\em the single vortex has spin half}. The vortex effective mass and spin-orbit coupling are extracted by diagonalizing the Hamiltonian on a 4x4 lattice. For two vortices, numerical `vortex-spin' correlations and orbital symmetries are consistent with Fermi and not Bose statistics. We discuss implications of the our results on the `vortex metal' phase at large magnetic fields.