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

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Cited by in corpus (9)

• 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
• Pretopological fractional excitations in the two-leg flux ladder
• Chiral SU(2)_k currents as local operators in vertex models and spin chains
• Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study
• How SU(2)${}_4$ Anyons are Z${}_3$ Parafermions
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• Twofold twist defect chains at criticality