Fractional charge (and statistics) in Luttinger liquids

TL;DR

This paper explores charge fractionalization in one-dimensional Luttinger liquids, examining whether non-integer charges can be considered sharp in gapless systems, and compares this phenomenon to gapped systems.

Contribution

It provides a detailed analysis of charge fractionalization in gapless Luttinger liquids, clarifying its nature and implications compared to gapped systems.

Findings

Charge fractionalization occurs in gapless Luttinger liquids.

Non-integer charges can be considered sharp under certain conditions.

Comparison between fractionalization in gapped and gapless systems.

Abstract

Charge fractionalization is the phenomenon where quasi-particle excitations in a many-particle system appear with non-integer values relative to the fundamental charge unit. Examples of such systems are known from field theoretical models and from physical realizations. Recently there has been an interest in charge fractionalization in one-dimensional systems described by Luttinger liquid theory. These are gapless systems and that gives rise to the question whether non-integer charges should be regarded as sharp in the same meaning as in a gapped system. In this talk I first give an introduction to charge fractionalization as an effect in gapped systems and discuss next in what sense the charge fractionalization effect is found in gapless Luttinger liquids. The talk is based on a recent paper with Mats Horsdal and Thors Hans Hansson.