Quantum Hall Effect in a Holographic Model

We consider a holographic description of a system of strongly coupled fermions in 2+1 dimensions based on a D7-brane probe in the background of D3-branes, and construct stable embeddings by turning on worldvolume fluxes. We study the system at finite temperature and charge density, and in the presence of a background magnetic field. We show that Minkowski-like embeddings that terminate above the horizon describe a family of quantum Hall states with filling fractions that are parameterized by a single discrete parameter. The quantization of the Hall conductivity is a direct consequence of the topological quantization of the fluxes. When the magnetic field is varied relative to the charge density away from these discrete filling fractions, the embeddings deform continuously into black-hole-like embeddings that enter the horizon and that describe metallic states. We also study the thermodynamics of this system and show that there is a first order phase transition at a critical temperature from the quantum Hall state to the metallic state.Comment: v2: 27 pages, 12 figures. There is a major revision in the quantitative analysis. The qualitative results and conclusions are unchanged, with one exception: we show that the quantum Hall state embeddings, which exist for discrete values of the filling fraction, deform continuously into metallic state embeddings away from these filling fraction