Holographic charge density waves

We show that strongly coupled holographic matter at finite charge density can exhibit charge density wave phases which spontaneously break translation invariance while preserving time-reversal and parity invariance. We show that such phases are possible within Einstein-Maxwell-dilaton theory in general spacetime dimensions. We also discuss related spatially modulated phases when there is an additional coupling to a second vector field, possibly with non-zero mass. We discuss how these constructions, and others, should be associated with novel spatially modulated ground states.