Phase diagram of an extended parafermion chain

TL;DR

This paper explores the phase diagram of an extended parafermion chain, revealing multiple gapped and gapless phases, including a topological phase with degenerate ground states, and discusses potential experimental realizations.

Contribution

It introduces an extended parafermion chain model with four-site interactions and maps it to a known Potts model, expanding understanding of its phase diagram.

Findings

Identification of multiple gapped phases including topological ones

Discovery of a gapless Luttinger-liquid phase

Potential for experimental realization using hetero-nanostructures

Abstract

We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin--Kadanoff transformation the parafermion chain is shown to be equivalent to the non-chiral $\mathbb{Z}_3$ axial next-nearest neighbour Potts model. We discuss a possible experimental realisation using hetero-nanostructures. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase.