AdS/QHE: towards a holographic description of quantum Hall experiments

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. Nonuniversal 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.

Holographic anyonic superfluidity

“…The application of SL(2, Z) (or some subgroup of it) to quantum Hall systems has a long history, 4 and recently SL(2, Z) duality has been incorporated in holographic quantum Hall models [29,30]. To understand the role of SL(2, Z), let us start with a quantum Hall state, with the conductivity given by (38) and (39) and gapped to neutral excitations.…”

A comment on holographic Luttinger theorem

“…Explicit solutions (such as the ones with horizons studied in, for examples, [22] - [34] ) are not necessary in the following. In the second line of the action (2.1), we have the parity-violating θ-term (the axion coupling), which is relevant for a quantum Hall effect under the magnetic field, see for examples, [29,[35][36][37][38].…”

Unconventional fusion and braiding of topological defects in a lattice model

“…Congruence subgroups have already studied in physical context of modular duality in quantum Hall plateau transition [123][124][125] and abelian gauge theory 126 . In addition to the congruent relations, we also find that S and T have finite orders that depend on k. For the twofold defects considered in this article, S k = 1 and T k = 1 for odd k or T 2k = 1 for even k. We demonstrate the different group structures for small k. We assume the twofold defects have color χ = B.…”