Bosonization of One-Dimensional Exclusons and Characterization of Luttinger Liquids

TL;DR

This paper develops a bosonization approach for one-dimensional exclusion gases, linking them to Luttinger liquids and providing a new conformal field theory perspective on their critical properties.

Contribution

It introduces a bosonization method for exclusion gases, establishing a direct connection to Luttinger liquids and their fixed points in one dimension.

Findings

Ideal excluson gases reproduce Luttinger liquid properties at low temperatures

The conformal field theory has a compactified radius related to exclusion statistics

Generalized gases exhibit similar critical behavior controlled by an effective statistics

Abstract

We achieve a bosonization of one-dimensional ideal gas of exclusion statistics $\lambda$ at low temperatures, resulting in a new variant of $c=1$ conformal field theory with compactified radius $R=\sqrt{1/\lambda}$. These ideal excluson gases exactly reproduce the low-$T$ critical properties of Luttinger liquids, so they can be used to characterize the fixed points of the latter. Generalized ideal gases with mutual statistics and non-ideal gases with Luttinger-type interactions have also similar behavior, controlled by an effective statistics varying in a fixed-point line.