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 (33)

• Fault-tolerant quantum computation by anyons
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• The density-matrix renormalization group in the age of matrix product states
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• String-net condensation: A physical mechanism for topological phases
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Conditions for a class of entanglement transformations
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Reduced density matrices and entanglement entropy in free lattice models
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Topological phases with parafermions: theory and blueprints
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Three-dimensional topological lattice models with surface anyons
• A short introduction to Fibonacci anyon models
• Approximate transformations and robust manipulation of bipartite pure state entanglement
• Generalizations and limitations of string-net models
• Exotic circuit elements from zero-modes in hybrid superconductor/quantum Hall systems
• Topological phases in gapped edges of fractionalized systems
• Criticality in Translation-Invariant Parafermion Chains
• Non-Abelian statistics as a Berry phase in exactly solvable models
• Parafermionic clock models and quantum resonance
• Optimal free descriptions of many-body theories
• Walker-Wang models and axion electrodynamics
• Entropic Topological Invariants in Three Dimensions
• Matrix product states for topological phases with parafermions
• Diagnosing Topological Edge States via Entanglement Monogamy

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• Correlation paradox of the dissociation limit: A quantum information perspective
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• Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
• Quantifying the efficiency of state preparation via quantum variational eigensolvers
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Parafermionic generalization of the topological Kondo effect
• Geometric description of the Kitaev honeycomb lattice model
• Quantifying the effect of interactions in quantum many-body systems
• Topological contextuality and anyonic statistics of photonic-encoded parafermions
• Interaction distance in the extended XXZ model
• Quantifying fermionic interactions from the violation of Wick's theorem
• Persistent non-Gaussian correlations in out-of-equilibrium Rydberg atom arrays
• Efficiency of free auxiliary models in describing interacting fermions: from the Kohn-Sham model to the optimal entanglement model
• Machine Learning Entanglement Freedom Or: How I Learned to Stop Worrying and Love Linear Regression
• Free fermion representation of the topological surface code
• Noninteracting tight-binding models for Fock parafermions