Quantum Hall Effect in a Holographic Model

TL;DR

This paper models quantum Hall states using holography, showing how stable D-brane embeddings correspond to quantized Hall conductance and phase transitions to metallic states at finite temperature.

Contribution

It introduces a holographic model with stable D7-brane embeddings that represent quantum Hall states with quantized conductance and analyzes phase transitions to metallic states.

Findings

Quantum Hall states are described by Minkowski-like embeddings with quantized fluxes.

Varying magnetic field leads to continuous deformation into metallic states.

A first-order phase transition occurs from quantum Hall to metallic states at a critical temperature.

Abstract

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.