Universality in Quantum Hall Systems: Coset Construction of Incompressible States

TL;DR

This paper explores the description of incompressible Quantum Hall fluids using two-dimensional chiral conformal field theories, introducing a coset construction method to generate candidate states with specific Hall conductivities.

Contribution

It develops a new framework linking topological field theories and CCFTs, providing a coset construction algorithm for modeling Quantum Hall states.

Findings

Derived consistency conditions for CCFTs describing QHF's

Presented a coset construction algorithm using simple currents

Provided explicit examples with specific Hall conductivities

Abstract

Incompressible Quantum Hall fluids (QHF's) can be described in the scaling limit by three-dimensional topological field theories. Thanks to the correspondence between three-dimensional topological field theories and two dimensional chiral conformal field theories (CCFT's), we propose to study QHF's from the point of view of CCFT's. We derive consistency conditions and stability criteria for those CCFT's that can be expected to describe a QHF. A general algorithm is presented which uses simple currents to construct interesting examples of such CCFT's. It generalizes the description of QHF's in terms of Quantum Hall lattices. Explicit examples, based on the coset construction, provide candidates for the description of Quantum Hall fluids with Hall conductivity s_H=1/2 e^2/h, 1/4 e^2/h, 3/5 e^2/h, e^2/h,...