Free-fermion descriptions of parafermion chains and string-net models

Abstract

Topological phases of matter remain a focus of interest due to their unique properties -- fractionalisation, ground state degeneracy, and exotic excitations. While some of these properties can occur in systems of free fermions, their emergence is generally associated with interactions between particles. Here we quantify the role of interactions in general classes of topological states of matter in all spatial dimensions, including parafermion chains and string-net models. Using the interaction distance [Nat. Commun. 8, 14926 (2017)], we measure the distinguishability of states of these models from those of free fermions. We find that certain topological states can be exactly described by free fermions, while others saturate the maximum possible interaction distance. Our work opens the door to understanding the complexity of topological models and to applying new types of fermionisation procedures to describe their low-energy physics.

10 pages, 10 figures

References in corpus (9)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• General Monogamy Inequality for Bipartite Qubit Entanglement
• A short introduction to Fibonacci anyon models
• Criticality in Translation-Invariant Parafermion Chains
• Non-Abelian statistics as a Berry phase in exactly solvable models
• Parafermionic clock models and quantum resonance
• Walker-Wang models and axion electrodynamics
• Matrix product states for topological phases with parafermions

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