Matrix product states for topological phases with parafermions

Abstract

In the Fock representation, we propose a framework to construct the generalized matrix product states (MPS) for topological phases with ${\mathbb{Z}}_p$ parafermions. Unlike the ${\mathbb{Z}}_2$ Majorana fermions, the parafermions form intrinsically interacting systems. Here we explicitly construct two topologically distinct classes of irreducible parafermionic MPS wave functions, characterized by one or two parafermionic zero modes at each end of an open chain. Their corresponding parent Hamiltonians are found as the fixed point models of the single ${\mathbb{Z}}_3$ parafermion chain and two-coupled parafermion chains with ${\mathbb{Z}}_3\times {\mathbb{Z}}_3$ symmetry. Our results thus pave the road to investigate all possible topological phases with ${\mathbb{Z}}_p$ parafermions within the matrix product representation in one dimension.

10 pages, 4 figures, published version

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Cited by in corpus (16)

• Non-Hermitian Physics
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
• Exact ground states for interacting Kitaev chains
• Fermionic tensor network methods
• Free-fermion descriptions of parafermion chains and string-net models
• Exact results for a $Z_3$ clock-type model and some close relatives
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• Tensor-network approach to compute genuine multisite entanglement in infinite quantum spin chains
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• 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
• Parafermionic representation of Potts-based cluster chain
• Noninteracting tight-binding models for Fock parafermions