The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems

TL;DR

This paper derives a chiral Tomonaga-Luttinger model for multi-layer fractional quantum Hall edges from Chern-Simons theory, describing their excitations and tunneling properties in and out of equilibrium.

Contribution

It introduces a new derivation of the edge model for multi-layer fractional quantum Hall systems using Chern-Simons theory, extending understanding of edge dynamics.

Findings

Tunneling exponent is insensitive to edge details for nu=m/(pm + 1).

Tunneling exponent decreases out of equilibrium for nu=m/(pm - 1).

The model applies to single-layer fractional quantum Hall states.

Abstract

Wen's chiral Tomonaga-Luttinger model for the edge of an m-layer quantum Hall system of total filling factor nu=m/(pm +- 1) with even p, is derived as a random-phase approximation of the Chern-Simons theory for these states. The theory allows for a description of edges both in and out of equilibrium, including their collective excitation spectrum and the tunneling exponent into the edge. While the tunneling exponent is insensitive to the details of a nu=m/(pm + 1) edge, it tends to decrease when a nu=m/(pm - 1) edge is taken out of equilibrium. The applicability of the theory to fractional quantum Hall states in a single layer is discussed.