A holographic anisotropic Dirac semimetal model

We introduce a holographic model for a Dirac semimetal in 2 + 1 dimensions that undergoes a topological phase transition. The model is based on deforming a relativistic UV fixed point with relevant operators that explicitly break rotational and internal symmetries. We map out the phase diagram for different values of the coupling constants. Each phase is distinguished by unique dispersion relations for probe fermions in the AdS geometry. We identify semi-metallic phases with Dirac cones, as well as an insulating phase with a mass gap and mild anisotropy. Notably, we also discover an anisotropic semi-Dirac phase where fermionic excitations are massless and exhibit linear dispersion in one direction and quadratic dispersion in the other.