Density wave super solid and Mott insulator-superfluid transition in presence of an artificial gauge field : Mean field and Strong Coupling results

We study the effect of an artificial gauge field on the zero
temperature phase diagram of extended Bose Hubbard model, that
describes ultra cold atoms in optical lattices with long range
interaction using mean field and strong coupling perturbation
theory. We determine analytically the effect of the artificial gauge
field on the density wave - supersolid (DW-SS) and the the Mott
insulator-superfluid (MI -SF) transition boundary. The momentum
distribution at these two transition boundaries is also calculated in
this approach. It is shown that such momentum distribution which can
be observed in time of flight measurement, reveals the symmetry of the
gauge potential through the formation of magnetic Brillouin zone and
clearly distinguishes between the DW-SS and MI-SF boundary. We also
point out that in symmetric gauge the momentum distribution structure
at these transition boundaries bears distinctive signatures of
vortices in supersolid and superfluid phases.