Loop Current and Antiferromagnetic States in Fermionic Hubbard Model with Staggered Flux at Half Filling

Anticipating realization of interacting fermions in an optical lattice with a large gauge field, we consider phase transitions and loop currents in a two-dimensional S=1/2 fermionic-Hubbard model with $\pi$/2-staggered flux at half filling. We use a variational Monte Carlo method, which is reliable even for strong correlations. As a trial wave function, a coexistent state of antifferomagnetic and staggered-flux orders is studied. In a strongly correlated regime, the ground state becomes an insulating coexistent state with loop currents. By comparing fermions with bosons, we discuss an important role of Pauli principle.