On the AdS/BCFT Approach to Quantum Hall Systems

TL;DR

This paper explores a holographic gravity model for quantum Hall systems using AdS/BCFT, revealing constant Hall conductivity, relations between thermal and electric conductivities, and the need for more complex models to capture realistic quantum Hall behavior.

Contribution

It introduces a simple AdS/BCFT holographic model for quantum Hall systems, analyzing its properties and limitations, and suggests the necessity of more general solutions for realistic modeling.

Findings

Hall conductivity is inversely proportional to topological coefficients.

Thermal and electric conductivities obey Wiedemann-Franz law at low temperatures.

Tensionless RS branes lead to gapless systems, indicating instability for quantum Hall modeling.

Abstract

In this paper we study a simple gravity model dual to a (2+1)-dimensional system with a boundary at finite charge density and temperature. In our naive AdS/BCFT extension of a well known AdS/CFT system a non-zero charge density must be supported by a magnetic field. As a result, the Hall conductivity is a constant inversely proportional to the coefficients of pertinent topological terms. Since the direct conductivity vanishes, such behaviors resemble that of a quantum Hall system with Fermi energy in the gap between the Landau levels. We further analyze the properties stemming from our holographic approach to a quantum Hall system. We find that at low temperatures the thermal and electric conductivities are related through the Wiedemann-Franz law, so that every charge conductance mode carries precisely one quantum of the heat conductance. From the computation of the edge currents we learn that the naive holographic model is dual to a gapless system if tensionless RS branes are used in the AdS/BCFT construction. To reconcile this result with the expected quantum Hall behavior we conclude that gravity solutions with tensionless RS branes must be unstable, calling for a search of more general solutions. We briefly discuss the expected features of more realistic holographic setups.