Kitaev lattice models as a Hopf algebra gauge theory

DOI10.1007/s00220-017-2860-7zbMath1460.81064arXiv1607.01144OpenAlexW2473815413MaRDI QIDQ529984

Catherine Meusburger

Publication date: 9 June 2017

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.01144

Mathematics Subject Classification ID

Quantum field theory on lattices (81T25) Topological field theories in quantum mechanics (81T45) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Hopf algebras and their applications (16T05)

Related Items (17)

Quantum double aspects of surface code models ⋮ Quantum and braided ZX calculus* ⋮ On entanglement entropy in non-abelian lattice gauge theory and 3D quantum gravity ⋮ Poisson-geometric analogues of Kitaev models ⋮ Quantum geometry of Boolean algebras and de Morgan duality ⋮ Boundary and domain wall theories of 2d generalized quantum double model ⋮ Algebraic aspects of boundaries in the Kitaev quantum double model ⋮ Modified toric code models with flux attachment from Hopf algebra gauge theory ⋮ Fusion basis for lattice gauge theory and loop quantum gravity ⋮ On weak Hopf symmetry and weak Hopf quantum double model ⋮ Quasi-local holographic dualities in non-perturbative 3d quantum gravity. I: Convergence of multiple approaches and examples of Ponzano-Regge statistical duals ⋮ Unnamed Item ⋮ Semidual Kitaev lattice model and tensor network representation ⋮ Mapping class group actions from Hopf monoids and ribbon graphs ⋮ Kitaev's stabilizer code and chain complex theory of bicommutative Hopf algebras ⋮ Integrals along bimonoid homomorphisms ⋮ Integrality, duality and finiteness in combinatoric topological strings

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