AdS/QHE: Towards a Holographic Description of Quantum Hall Experiments

TL;DR

This paper proposes a holographic model based on AdS/CFT correspondence that captures key features of quantum Hall systems, including duality relations, plateaux, and semi-circle transitions, providing a new theoretical framework for understanding quantum Hall phenomena.

Contribution

It introduces a simple holographic model with nonzero DC conductivity that reproduces quantum Hall duality features and transitions, advancing the theoretical understanding of these systems.

Findings

Model exhibits duality and semi-circle laws

Reproduces quantum Hall plateaux and transitions

Provides a strongly coupled analog of composite boson picture

Abstract

Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semi-circle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the DC ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero DC conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semi-circle transitions between them. The model can be regarded as a strongly coupled analog of the old `composite boson' picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model.