Luttinger liquids, Fermi liquids and fractional statistics

TL;DR

This paper explores how one-dimensional interacting fermion systems, described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional charge and statistics, using a Landau Fermi liquid approach.

Contribution

It demonstrates that the quasiparticles in Luttinger liquids can be viewed as fractionalized particles with generalized exclusion statistics through a change of variables and interaction parameters.

Findings

Quasiparticles exhibit fractional charge.

Interaction parameters can be transformed to zero.

Quasiparticles obey generalized exclusion statistics.

Abstract

We discuss how one-dimensional interacting fermion systems, which in the low energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional charge and statistics. Our approach is to use Landau's phenomenological approach to Fermi liquid theory, where the quasiparticles are interpreted as adiabatically dressed fermions. In an earlier publication the local charge carried by these excitations has been shown to be fractional. We focus here on the statistics of the quasiparticles and show that by a change of momentum variables the Landau parameters of the generalized Fermi fluid can be transformed to zero. This change in interaction is compensated by a change of the entropy function, which is consistent with the interpretation of the quasiparticles as satisfying generalized exclusion statistics.