Topological phases of parafermions: a model with exactly-solvable ground states

TL;DR

This paper introduces a quasi-exactly-solvable model for a chain of parafermions exhibiting topological order, with analytically characterized ground states and signatures of topological phases, advancing understanding of non-approximate topological parafermionic systems.

Contribution

The paper presents a novel, quasi-exactly-solvable model for parafermionic chains with topological order, including explicit ground-state wavefunctions and analytical signatures of topological phases.

Findings

Ground states are matrix-product states with elegant Fock parafermion interpretation

Analytical demonstration of topological order signatures

Model applicable without strong edge modes, preserving symmetries

Abstract

Parafermions are emergent excitations that generalize Majorana fermions and can also realize topological order. In this paper we present a non-trivial and quasi-exactly-solvable model for a chain of parafermions in a topological phase. We compute and characterize the ground-state wave-functions, which are matrix-product states and have a particularly elegant interpretation in terms of Fock parafermions, reflecting the factorized nature of the ground states. Using these wavefunctions, we demonstrate analytically several signatures of topological order. Our study provides a starting point for the non-approximate study of topological one-dimensional parafermionic chains with spatial-inversion and time-reversal symmetry in the absence of strong edge modes.