Loop models and their critical points

Abstract

Loop models have been widely studied in physics and mathematics, in problems ranging from polymers to topological quantum computation to Schramm-Loewner evolution. I present new loop models which have critical points described by conformal field theories. Examples include both fully-packed and dilute loop models with critical points described by the superconformal minimal models and the SU(2)_2 WZW models. The dilute loop models are generalized to include SU(2)_k models as well.

20 pages, 15 figures

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• Solvable RSOS models based on the dilute BWM algebra
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Cited by in corpus (22)

• Interacting anyons in topological quantum liquids: The golden chain
• Fermionic minimal models
• Anyonic quantum spin chains: Spin-1 generalizations and topological stability
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
• Majorana Loop Models for Measurement-Only Quantum Circuits
• Critical exponents of domain walls in the two-dimensional Potts model
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• Critical points in coupled Potts models and critical phases in coupled loop models
• Logarithmic Superconformal Minimal Models
• An integrable modification of the critical Chalker-Coddington network model
• Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model
• Critical interfaces and duality in the Ashkin Teller model
• Geometrical properties of parafermionic spin models
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Bicolor loop models and their long range entanglement
• Electron Model on Truchet Tiling: Extended-to-Localized Transitions, Mobility Edge, and Asymmetric Spectrum
• Loop models for CFTs
• Approaching the RSOS critical points through entanglement: one model for many universalities
• A chain of strongly correlated SU(2)_4 anyons: Hamiltonian and Hilbert space of states
• One-Dimensional Sums and Finitized Characters of $2\times 2$ Fused RSOS Models
• Topology-driven phase transitions in the classical monomer-dimer-loop model
• Boundary conformal field theories and loop models