  Contrary to canonical expectations we show that lattice translational
symmetry breaking often accompanies uniformly ordered flux phases. We
demonstrate this phenomena by studying a spinless-fermion model on a square
latttice with nearest-neighbor repulsion. We find an array of flux patterns, as
a function interaction strength and filling factor, that break time-reversal
symmetry but may or may not preserve translational symmetry. A key finding is
that the pattern of flux ordering does not uniquely determine the electronic
properties. As such a class of new phases of matter are introduced that expand
the candidate ground states in many body interacting systems.
