Bond ordering in flux phases

We analyze bond current orders on a square lattice in a spinless-fermion model with nearest-neighbor repulsion. We find that time-reversal symmetry and translational symmetry can be broken by various interaction driven flux patterns, turned by interaction strength and the filling factor. Moreover, we point out that the interaction driven flux patterns do not uniquely determine the electronic properties as opposed to previous studied flux phases in different contexts such as t-J model and Heisenberg Hubbard model.