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Kitaev models based on unitary quantum groupoids. The complete set of infinite volume ground states for Kitaev's Abelian quantum double models. Matthew Cha, Pieter Naaijkens, and Bruno Nachtergaele. Remarks on entanglement entropy for gauge fields. Horacio Casini, Marina Huerta, and José Alejandro Rosabal. A hierarchy of topological tensor network states. Oliver Buerschaper, Juan Martín Mombelli, Matthias Christandl, and Miguel Aguado. Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models. Topological quantum order: stability under local perturbations. Sergey Bravyi, Matthew B Hastings, and Spyridon Michalakis. Communications in mathematical physics, 307 (3): 609, 2011. A short proof of stability of topological order under local perturbations. Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons. Journal of Physics A: Mathematical and Theoretical, 40 (24): 6451, 2007. A statistical mechanics view on Kitaev's proposal for quantum memories. Finally, we compute the topological entanglement entropy in Kitaev's model, and show, contrary to previous claims in the literature, that it does not depend on whether the ``log dim R'' term is included in the definition of entanglement entropy. Naaijkens (PhD thesis, 2012) under a different context can be adapted to provide another proof of the error correcting property of Kitaev's model. We also note that the methods developed by P. We contrast this result with the fact that local properties of gauge-invariant states are not generally determined by specifying all of their non-Abelian fluxes - that is, the Wilson loops of lattice gauge theory do not form a complete commuting set of observables. Alternatively, the local properties of a gauge-invariant state are fully determined by specifying that its holonomies in the region are trivial. Actually a stronger claim is shown: any two states with zero energy density in some contractible region must have the same reduced state in that region.
We offer an explicit proof that this is the case for arbitrary finite groups. In particular, the ground space is thought to yield a quantum error-correcting code. Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order.
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