Topological aspects of the critical three-state Potts model

Abstract

We explore the topological defects of the critical three-state Potts spin system on the torus, Klein bottle and cylinder. A complete characterization is obtained by breaking down the Fuchs-Runkel-Schweigert construction of 2d rational CFT to the lattice setting. This is done by applying the strange correlator prescription to the recently obtained tensor network descriptions of string-net ground states in terms of bimodule categories [Lootens, Fuchs, Haegeman, Schweigert, Verstraete, SciPost Phys. 10, 053 (2021)]. The symmetries are represented by matrix product operators (MPO), as well as intertwiners between the diagonal tetracritical Ising model and the non-diagonal three-state Potts model. Our categorical construction lifts the global transfer matrix symmetries and intertwiners, previously obtained by solving Yang-Baxter equations, to MPO symmetries and intertwiners that can be locally deformed, fused and split. This enables the extraction of conformal characters from partition functions and yields a comprehensive picture of all boundary conditions.

71 pages, many figures, includes supplementary material

References in corpus (12)

• Interacting anyons in topological quantum liquids: The golden chain
• Explicit tensor network representation for the ground states of string-net models
• Topological Defects on the Lattice: Dualities and Degeneracies
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Parafermionic conformal field theory on the lattice
• Microscopic models of interacting Yang-Lee anyons
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Universal entropy of conformal critical theories on a Klein bottle
• Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study
• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field
• Tensor-product representations for string-net condensed states
• Cardy states, defect lines and chiral operators of coset CFTs on the lattice

Cited by in corpus (23)

• Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
• Dualities in one-dimensional quantum lattice models: topological sectors
• A critical lattice model for a Haagerup conformal field theory
• Classifying phases protected by matrix product operator symmetries using matrix product states
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Disentangling critical quantum spin chains with Clifford circuits
• Strange correlators for topological quantum systems from bulk-boundary correspondence
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Universal scaling of Klein bottle entropy near conformal critical points
• Extracting the Luttinger parameter from a single wave function
• Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
• Duality via Sequential Quantum Circuit in the Topological Holography Formalism
• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Anyonic Chains -- $\alpha$-Induction -- CFT -- Defects -- Subfactors
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Crosscap states and duality of Ising field theory in two dimensions
• Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models
• Revisiting the symmetry-resolved entanglement for non-invertible symmetries in $1+1$d conformal field theories
• Systematic construction of stabilizer codes via gauging abelian boundary symmetries
• Les Houches Lecture Notes on Tensor Networks
• From gauging to duality in one-dimensional quantum lattice models
• Entropic order parameters and topological holography