Variational Study on Loop Currents in Bose Hubbard model with Staggered Flux

In view of strongly interacting bosons in an optical lattice with a large gauge field, we study phase transitions in a two-dimensional Bose-Hubbard model with a staggered flux, on the basis of variational Monte Carlo calculations. Inthe trial states,besides typical onsite and intersite correlation factors, we introduce a configuration-dependent phase factor,which was recently found essential for treating current-carrying states. It is found that this phase factor is qualitativelyvitalfordescribing a Mott insulating (MI) state in the present model. Thereby, the Peierls phasesattached in relevant hopping processes are cancelled out. As a result, local currents completely suppressed in MI states, namely, a chiral Mott state does not appear for the square lattice, in contrast tothecorresponding two-leg ladder model. In addition, we discuss other features of the first-order superfluid-MI transition in this model.