Fermi liquids and fractional statistics in one dimension

TL;DR

This paper demonstrates that one-dimensional interacting fermion systems, described by Luttinger liquid theory, can be reformulated as systems of particles with fractional exchange statistics, using Landau's Fermi liquid theory.

Contribution

It introduces a novel reformulation of 1D fermion systems as fractional statistics particles via Landau's Fermi liquid framework, including an application to quantum Hall boundary excitations.

Findings

Reformulation of 1D fermions as fractional statistics particles.

Application to boundary excitations in quantum Hall systems.

Insight into low-energy behavior of 1D interacting fermions.

Abstract

Interacting fermion systems in one dimension, which in the low energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional exchange statistics. This is shown by use of Landau's Fermi liquid theory, with quasiparticles interpreted as adiabatically dressed fermions. An application of this method is included, where boundary excitations of a two-dimensional quantum Hall electron system are studied.