SciPost Physics Core

SciPost Phys. Core 5, 008 (2022) · published 8 February 2022

• doi: 10.21468/SciPostPhysCore.5.1.008
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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.

• Teixeira et al., Overlap of parafermionic zero modes at a finite distance
  Phys. Rev. Research 4, 043094 (2022) [Crossref]
• Yu et al., Quantum criticality of a Z3 -symmetric spin chain with long-range interactions
  Phys. Rev. E 107, 054122 (2023) [Crossref]
• Nielsen et al., Dynamics of parafermionic states in transport measurements
  SciPost Phys. 15, 189 (2023) [Crossref]
• Sayyad et al., Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
  Phys. Rev. Research 5, L022046 (2023) [Crossref]
• Traverso et al., An exact local mapping from clock-spins to fermions
  SciPost Phys. Core 6, 055 (2023) [Crossref]