Phase diagram of an extended parafermion chain

Abstract

We study the phase diagram of an extended parafermion chain, which,in addition to terms coupling parafermions on neighbouring sites, alsopossesses terms involving four sites. Via a Fradkin–Kadanofftransformation the parafermion chain is shown to be equivalent to thenon-chiral \mathbf{\mathbb{Z}_3}ℤ3axial next-nearest neighbour Potts model. We discuss a possibleexperimental realisation using hetero-nanostructures. The phase diagramcontains several gapped phases, including a topological phase where thesystem possesses three (nearly) degenerate ground states, and a gaplessLuttinger-liquid phase.