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

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.

6 + 9 pages, 3 figures

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Cited by in corpus (31)

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• Z4 parafermions in one-dimensional fermionic lattices
• Parafermionic clock models and quantum resonance
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Pretopological fractional excitations in the two-leg flux ladder
• Exact ground states for interacting Kitaev chains
• Localization-enhanced and degraded topological-order in interacting p-wave wires
• Parafermionization, bosonization, and critical parafermionic theories
• Exact results for a $Z_3$ clock-type model and some close relatives
• Matrix product states for topological phases with parafermions
• Topological protection of Majorana polaritons in a cavity
• Bosonization for fermions and parafermions
• Dyonic zero-energy modes
• Dynamical topological excitations in parafermion chains
• Quantum dots as parafermion detectors
• Almost Strong Zero Modes at Finite Temperature
• Edge ${\mathbb{Z}}_3$ parafermions in fermionic lattices
• Decoding quantum criticalities from fermionic/parafermionic topological states
• Classifying parafermionic gapped phases using matrix product states
• Anomalous Quantum Information Scrambling for ${\mathbb{Z}}_3$ Parafermion Chains
• Enriched classification of parafermionic gapped phases with time reversal symmetry
• Quantum-vacuum-protected topological edge polaritons
• Interrelations among frustration-free models via Witten's conjugation
• Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model
• Overlap of parafermionic zero modes at a finite distance
• Engineering a Josephson junction chain for the simulation of the clock model
• Nonuniform Parafermion Chains: Low-Energy Physics and Finite-Size Effects
• Noninteracting tight-binding models for Fock parafermions
• Edge-Edge Correlations without Edge-States: $\eta$-clustering State as Ground State of the Extended Attractive SU(3) Hubbard Chain