Electric-magnetic duality of lattice systems with topological order

DOI10.1016/j.nuclphysb.2013.08.014zbMath1284.81355arXiv1006.5823OpenAlexW1981610565MaRDI QIDQ2440225

Matthias Christandl, Liang Kong, Oliver Buerschaper, Miguel Aguado

Publication date: 27 March 2014

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.5823

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Many-body theory; quantum Hall effect (81V70) Topological field theories in quantum mechanics (81T45) Hopf algebras and their applications (16T05) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (16)

From 3D topological quantum field theories to 4D models with defects ⋮ Ribbon operators in the generalized Kitaev quantum double model based on Hopf algebras ⋮ A decomposition of the Brauer-Picard group of the representation category of a finite group ⋮ Boundary and domain wall theories of 2d generalized quantum double model ⋮ Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries ⋮ Anyon condensation and tensor categories ⋮ Fusion basis for lattice gauge theory and loop quantum gravity ⋮ On weak Hopf symmetry and weak Hopf quantum double model ⋮ Quantum gravity kinematics from extended TQFTs ⋮ Quantum double models coupled to matter fields: A detailed review for a dualization procedure ⋮ Semidual Kitaev lattice model and tensor network representation ⋮ First-order formulation of teleparallel gravity and dual loop gravity ⋮ Quantum geometry from higher gauge theory ⋮ Kitaev models based on unitary quantum groupoids ⋮ On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories ⋮ Generalized cluster states based on finite groups

Cites Work

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• SOME UNIVERSAL PROPERTIES OF LEVIN-WEN MODELS
• Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States
• Quantised singularities in the electromagnetic field,
• A hierarchy of topological tensor network states
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