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Crystalline Scaling Geometries from Vortex Lattices

We study magnetic geometries with Lifshitz and/or hyperscaling violation exponents (both with a hard wall cutoff in the IR and a smooth black brane horizon) which have a complex scalar field which couples to the magnetic field. The complex scalar is unstable to the production of a vortex lattice in the IR. The lattice is a normalizable mode which is relevant (i.e. grows into the IR.) When one considers linearized backreaction of the lattice on the metric and gauge field, the metric forms a crystalline structure. We analyze the scaling of the free energy, thermodynamic entropy, and entanglement in the lattice phase and find that in the smeared limit, the leading order correction to thermodynamic properties due to the lattice has the scaling behavior of a theory with a hyperscaling violation exponent between 0 and 1, indicating a flow to an effectively lower-dimensional theory in the deep IR.