# Quantum Hall Effect in a Holographic Model - High Energy Physics - Theory

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Abstract: We consider a holographic description of a system of strongly coupledfermions in 2+1 dimensions based on a D7-brane probe in the background ofD3-branes, and construct stable embeddings by turning on worldvolume fluxes. Westudy the system at finite temperature and charge density, and in the presenceof a background magnetic field. We show that Minkowski-like embeddings thatterminate above the horizon describe a family of quantum Hall states withfilling fractions that are parameterized by a single discrete parameter. Thequantization of the Hall conductivity is a direct consequence of thetopological quantization of the fluxes. When the magnetic field is variedrelative to the charge density away from these discrete filling fractions, theembeddings deform continuously into black-hole-like embeddings that enter thehorizon and that describe metallic states. We also study the thermodynamics ofthis system and show that there is a first order phase transition at a criticaltemperature from the quantum Hall state to the metallic state.

Author: ** Oren Bergman, Niko Jokela, Gilad Lifschytz, Matthew Lippert**

Source: https://arxiv.org/