Parafermionic conformal field theory on the lattice

Abstract

Finding the precise correspondence between lattice operators and the continuum fields that describe their long-distance properties is a largely open problem for strongly interacting critical points. Here we solve this problem essentially completely in the case of the three-state Potts model, which exhibits a phase transition described by a strongly interacting 'parafermion' conformal field theory. Using symmetry arguments, insights from integrability, and extensive simulations, we construct lattice analogues of nearly all the relevant and marginal physical fields governing this transition. This construction includes chiral fields such as the parafermion. Along the way we also clarify the structure of operator product expansions between order and disorder fields, which we confirm numerically. Our results both suggest a systematic methodology for attacking non-free field theories on the lattice and find broader applications in the pursuit of exotic topologically ordered phases of matter.

27 pages, 4 figures; v2 added references

References in corpus (28)

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• The density-matrix renormalization group
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• From density-matrix renormalization group to matrix product states
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Parafermionic edge zero modes in Z_n-invariant spin chains
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• Conformal invariance of lattice models
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• Conformal loop ensembles and the stress-energy tensor
• Discretely Holomorphic Parafermions in Lattice Z(N) Models
• The Many Faces of the Chiral Potts Model
• Discrete Holomorphicity at Two-Dimensional Critical Points
• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice
• Identification of the stress-energy tensor through conformal restriction in SLE and related processes
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Cited by in corpus (55)

• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Topological phases with parafermions: theory and blueprints
• Lattice supersymmetry and order-disorder coexistence in the tricritical Ising model
• Disorder Operators and their Descendants
• Mapping topological to conformal field theories through strange correlators
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Criticality in Translation-Invariant Parafermion Chains
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Realizing all $so(N{)}_1$ quantum criticalities in symmetry protected cluster models
• Fermionized parafermions and symmetry-enriched Majorana modes
• Z4 parafermions in one-dimensional fermionic lattices
• Topological phases of parafermions: a model with exactly-solvable ground states
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Designer non-Abelian anyon platforms: from Majorana to Fibonacci
• Pretopological fractional excitations in the two-leg flux ladder
• Topological aspects of the critical three-state Potts model
• Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
• The "not-A", RSPT and Potts phases in an $S_3$-invariant chain
• Galois conjugated tensor fusion categories and non-unitary CFT
• Tunable Splitting of the Ground-State Degeneracy in 1D Parafermionic Wires
• Quantifying the efficiency of state preparation via quantum variational eigensolvers
• Non-diagonal anisotropic quantum Hall states
• Qutrit Toric Code and Parafermions in Trapped Ions
• Relaxation and entropy generation after quenching quantum spin chains
• Bosonization for fermions and parafermions
• Multipartite entanglement and quantum Fisher information in conformal field theories
• Chiral SU(2)_k currents as local operators in vertex models and spin chains
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Coulomb Blockade in Fractional Topological Superconductors
• Integrability and braided tensor categories
• Quantum criticality in many-body parafermion chains
• Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study
• Quantum simulation of the tricritical Ising model in tunable Josephson junction ladders
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• The Lattice-Continuum Correspondence in the Ising Model
• Boundary transitions from a single round of measurements on gapless quantum states
• How SU(2)${}_4$ Anyons are Z${}_3$ Parafermions
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• On quenches to the critical point of the three states Potts model -- Matrix Product State simulations and CFT
• The Ultraviolet Structure of Quantum Field Theories. Part 2: What is Quantum Field Theory?
• Twofold twist defect chains at criticality
• Conformal Field Theories as Scaling Limit of Anyonic Chains
• Enriched classification of parafermionic gapped phases with time reversal symmetry
• An exact local mapping from clock-spins to fermions
• Melting of three-sublattice order in triangular lattice Ising antiferromagnets: Power-law order, $Z_6$ parafermionic multicriticality, and weakly first order transitions
• Engineering a Josephson junction chain for the simulation of the clock model
• Chiral spin liquid in a generalized Kitaev honeycomb model with ${\mathbb{Z}}_4$ 1-form symmetry
• ${\mathbb{Z}}_3$ Parafermionic Chain Emerging From Yang-Baxter Equation
• Confinement and Flux Attachment
• Energy transport in Z3 chiral clock model
• Phase diagram of an extended parafermion chain
• Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures
• Universal Euler-Cartan Circuits for Quantum Field Theories