Z4 parafermions in one-dimensional fermionic lattices

TL;DR

This paper introduces a new exactly solvable one-dimensional fermionic model hosting stable Z4 parafermionic zero modes, advancing understanding of topological phases relevant for quantum computation.

Contribution

It presents a novel mapping between Z4 parafermions and spin-1/2 fermions, enabling the construction of a local, interacting Hamiltonian with parafermionic zero modes.

Findings

The model hosts zero-energy parafermionic modes.

The parafermionic phase is stable over a wide parameter range.

Signatures of the phase are observed in the spectral function.

Abstract

Parafermions are emergent excitations which generalize Majorana fermions and are potentially relevant to topological quantum computation. Using the concept of Fock parafermions, we present a mapping between lattice $\mathbb{Z}_4$ parafermions and lattice spin-$1/2$ fermions which preserves the locality of operators with $\mathbb{Z}_4$ symmetry. Based on this mapping, we construct an exactly solvable, local, and interacting one-dimensional fermionic Hamiltonian which hosts zero-energy modes obeying parafermionic algebra. We numerically show that this parafermionic phase remains stable in a wide range of parameters, and discuss its signatures in the fermionic spectral function.