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

TL;DR

The paper addresses how to model quantum Hall transitions within AdS/CFT by enforcing an emergent duality group on low-energy transport. It develops a dilaton-DBI holographic framework in which an $SL(2,R)$ (broken to a discrete subgroup) acts on the axio-dilaton and gauge sector, yielding nonzero DC conductivities and duality-covariant transport. Conductivities transform under modular actions, producing plateaux and semicircular transition curves that mirror experimental QHE phenomenology, including the $ ext{Γ}_0(2)$ (or related) duality structure. The work provides a new strongly coupled platform to study QHE, delivering clear predictions for DC transport and scaling behavior while outlining necessary extensions to reach quantitative agreement with real materials.

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.