Abelian Hall Fluids and Edge States: a Conformal Field Theory Approach

TL;DR

This paper uses conformal field theory to comprehensively describe abelian Hall fluids, including their ground states, excitations, and edge dynamics, highlighting differences in Jain's sequences with extended symmetries.

Contribution

It introduces a Coulomb gas vertex operator approach to model abelian Hall fluids and their edge states, emphasizing the role of extended algebras in Jain's sequences.

Findings

Complete description of ground states on planar and toroidal geometries.

Characterization of low energy excitation spectrum.

Identification of extended algebra structures in Jain's sequences.

Abstract

We show that a Coulomb gas Vertex Operator representation of 2D Conformal Field Theory gives a complete description of abelian Hall fluids: as an euclidean theory in two space dimensions leads to the construction of the ground state wave function for planar and toroidal geometry and characterizes the spectrum of low energy excitations; as a $1+1$ Minkowski theory gives the corresponding dynamics of the edge states. The difference between a generic Hall fluid and states of the Jain's sequences is emphasized and the presence, in the latter case, of of an $\hat {U}(1)\otimes \hat {SU}(n)$ extended algebra and the consequent propagation on the edges of a single charged mode and $n-1$ neutral modes is discussed.