Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing

TL;DR

This paper explores a one-dimensional fermionic model with even multiplet pairing that supports non-local parafermions, revealing a coexistence of topological degeneracy and spontaneous symmetry breaking, with potential implications for fractional Josephson effects.

Contribution

It introduces a novel fermionic model with non-local parafermions and analyzes their properties, including the coexistence of topological degeneracy and symmetry breaking.

Findings

Supports non-local parafermions instead of boundary operators

Ground state degeneracy is partly topological and coexists with symmetry breaking

For N=4, exhibits dual of an 8π fractional Josephson effect

Abstract

We discuss a one-dimensional fermionic model with a generalized $\mathbb{Z}_{N}$ even multiplet pairing extending Kitaev $\mathbb{Z}_{2}$ chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a $\mathbb{Z}_{N}$ symmetry enforcing an $N$-fold degenerate ground state robust to certain disorder. Interestingly, we show that the system supports a pair of parafermions but they are non-local instead of being boundary operators. As a result, the degeneracy of the ground state is only partly topological and coexists with spontaneous symmetry breaking by a (two-particle) pairing field. Each symmetry-breaking sector is shown to possess a pair of Majorana edge modes encoding the topological twofold degeneracy. Surrounded by two band insulators, the model exhibits for $N=4$ the dual of an $8 \pi$ fractional Josephson effect highlighting the presence of parafermions.