Galois conjugated tensor fusion categories and non-unitary CFT

Abstract

We provide a generalisation of the matrix product operator (MPO) formalism for string-net projected entangled pair states (PEPS) to include non-unitary solutions of the pentagon equation. These states provide the explicit lattice realisation of the Galois conjugated counterparts of (2+1) dimensional TQFTs, based on tensor fusion categories. Although the parent Hamiltonians of these renormalisation group fixed point states are non-Hermitian, many of the topological properties of the states still hold, as a result of the pentagon equation. We show by example that the the topological sectors of the Yang-Lee theory (the non-unitary counterpart of the Fibonacci fusion category) can be constructed even in the absence of closure under Hermitian conjugation of the basis elements of the Ocneanu tube algebra. We argue that this can be generalised to the non-unitary solutions of all $SU(2)$ level $k$ models. The topological sector construction is demonstrated by applying the concept of strange correlators to the Yang-Lee model, giving rise to a non-unitary version of the classical hard hexagon model in the Yang-Lee universality class and obtaining all generalised twisted boundary conditions on a finite cylinder of the Yang-Lee edge singularity.

arXiv comment5 pages, 1 figure

References in corpus (23)

• Anyons in an exactly solved model and beyond
• String-net condensation: A physical mechanism for topological phases
• Interacting anyons in topological quantum liquids: The golden chain
• TFT construction of RCFT correlators I: Partition functions
• Generalised twisted partition functions
• Kramers-Wannier duality from conformal defects
• Variational optimization algorithms for uniform matrix product states
• Topological Defects on the Lattice I: The Ising model
• Anyons and matrix product operator algebras
• Explicit tensor network representation for the ground states of string-net models
• Quantum computation with Turaev-Viro codes
• Wave Function and Strange Correlator of Short Range Entangled states
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Conformal boundary conditions and three-dimensional topological field theory
• Anyonic Chains, Topological Defects, and Conformal Field Theory
• Mapping topological to conformal field theories through strange correlators
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Topological conformal defects with tensor networks
• Parafermionic conformal field theory on the lattice
• Microscopic models of interacting Yang-Lee anyons
• Galois Conjugates of Topological Phases
• Condensation-Driven Phase Transitions in Perturbed String Nets
• Clebsch-Gordan and 6j-coefficients for rank two quantum groups

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• Non-Hermitian Physics
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• Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
• Topological aspects of the critical three-state Potts model
• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Galois Orbits of TQFTs: Symmetries and Unitarity
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Galois Conjugation and Multiboundary Entanglement Entropy
• Galois conjugates of String-net Model
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Effective Conformal Field Theory generated from Pure and Dephased Chern insulator
• Virasoro Generators in the Fibonacci Model Tensor Network -- Tackling Finite Size Effects
• Les Houches Lecture Notes on Tensor Networks