Conformal field theory approach to gapless 1D fermion systems and application to the edge excitations of nu = 1/(2p+1) quantum Hall sequences

TL;DR

This paper develops a conformal field theory framework to describe gapless 1D fermion systems and applies it to quantum Hall edge states, providing exact correlation functions and insights into the underlying symmetries.

Contribution

It introduces a CFT approach to analyze edge excitations in quantum Hall systems, identifying the RCFT structure and physical operators for these edge states.

Findings

Correlation functions computed exactly at finite size and temperature

Edge excitations described by twisted Luttinger theories

Edge fermion operators identified as symmetry generators

Abstract

We present a comprehensive study of the effective Conformal Field Theory (CFT) describing the low energy excitations of a gas of spinless interacting fermions on a circle in the gapless regime (Luttinger liquid). Functional techniques and modular transformation properties are used to compute all correlation functions in a finite size and at finite temperature. Forward scattering disorder is treated exactly. Laughlin experiments on charge transport in a Quantum Hall Fluid on a cylinder are reviewed within this CFT framework. Edge excitations above a given bulk excitation are described by a twisted version of the Luttinger effective theory. Luttinger CFTs corresponding to the nu =1/(2p+1) filling fractions appear to be rational CFTs (RCFT). Generators of the extended symmetry algebra are identified as edge fermions creators and annihilators, thus giving a physical meaning to the RCFT point of view on edge excitations of these sequences.