  For collectively interacting repulsive particles driven on triangular
substrates, we show that for certain directions of drive a spontaneous symmetry
breaking phenomena occurs where the particles can flow in one of two directions
that are not aligned with the external drive, giving rise to a positive or
negative Hall current. Along these directions, the particle flow is highly
ordered, while in the direction of the drive the flow is disordered. We also
find a number of dynamical phase transitions and unusual hysteretic properties
that arise due to the symmetry breaking properties of the flows.
