Phase diagram for hard-core $\mathbb{Z}_3$ anyons on the ladder

TL;DR

This paper investigates the phase diagram of hard-core  anyons on a ladder, revealing unique behaviors and a new phase transition related to hole crystallization, with implications for all Abelian  models.

Contribution

It introduces the first numerical analysis of  anyons on a ladder, discovering a novel phase transition and providing extrapolations for all Abelian  models.

Findings

Identification of a new phase transition involving hole crystallization.

Qualitative predictions extended to all Abelian  anyon models.

Distinct behavior compared to bosons and fermions in low-dimensional systems.

Abstract

Studies of free particles in low-dimensional quantum systems such as two-leg ladders provide insight into the influence of statistics on collective behaviour. The behaviours of bosons and fermions are well understood, but two-dimensional systems also admit excitations with alternative statistics known as anyons. Numerical analysis of hard-core $\mathbb{Z}_3$ anyons on the ladder reveals qualitatively distinct behaviour, including a novel phase transition associated with crystallisation of hole degrees of freedom into a periodic foam. Qualitative predictions are extrapolated for all Abelian $\mathbb{Z}_q$ anyon models.