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arXiv · 1101.0527

From entanglement renormalisation to the disentanglement of quantum double models

Miguel Aguado
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Abstract

We describe how the entanglement renormalisation approach to topological lattice systems leads to a general procedure for treating the whole spectrum of these models, in which the Hamiltonian is gradually simplified along a parallel simplification of the connectivity of the lattice. We consider the case of Kitaev's quantum double models, both Abelian and non-Abelian, and we obtain a rederivation of the known map of the toric code to two Ising chains; we pay particular attention to the non-Abelian models and discuss their space of states on the torus. Ultimately, the construction is universal for such models and its essential feature, the lattice simplification, may point towards a renormalisation of the metric in continuum theories.

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Miguel Aguado. 2010-12-26. From entanglement renormalisation to the disentanglement of quantum double models. https://doi.org/10.1016/j.aop.2011.07.007

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