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Title: From entanglement renormalisation to the disentanglement of quantum double models

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. - Highlights: > The toric code is explicitly mapped to two Ising chains and their diagonalisation. > The procedure uses tensor network ideas, notably entanglement renormalisation. > The construction applies to all of Kitaev's non-Abelian quantum double models. > The algebraic structure of non-Abelian models is thoroughly discussed. > The construction is universal and may work on the metric in the continuum limit.

Authors:
Publication Date:
OSTI Identifier:
21583332
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 326; Journal Issue: 9; Other Information: DOI: 10.1016/j.aop.2011.07.007; PII: S0003-4916(11)00116-3; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAINS; HAMILTONIANS; ISING MODEL; METRICS; QUANTUM ENTANGLEMENT; RENORMALIZATION; SPECTRA; TENSORS; TOPOLOGY; CRYSTAL MODELS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATHEMATICS; QUANTUM OPERATORS

Citation Formats

Aguado, Miguel, E-mail: miguel.aguado@mpq.mpg.de. From entanglement renormalisation to the disentanglement of quantum double models. United States: N. p., 2011. Web. doi:10.1016/j.aop.2011.07.007.
Aguado, Miguel, E-mail: miguel.aguado@mpq.mpg.de. From entanglement renormalisation to the disentanglement of quantum double models. United States. doi:10.1016/j.aop.2011.07.007.
Aguado, Miguel, E-mail: miguel.aguado@mpq.mpg.de. Thu . "From entanglement renormalisation to the disentanglement of quantum double models". United States. doi:10.1016/j.aop.2011.07.007.
@article{osti_21583332,
title = {From entanglement renormalisation to the disentanglement of quantum double models},
author = {Aguado, Miguel, E-mail: miguel.aguado@mpq.mpg.de},
abstractNote = {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. - Highlights: > The toric code is explicitly mapped to two Ising chains and their diagonalisation. > The procedure uses tensor network ideas, notably entanglement renormalisation. > The construction applies to all of Kitaev's non-Abelian quantum double models. > The algebraic structure of non-Abelian models is thoroughly discussed. > The construction is universal and may work on the metric in the continuum limit.},
doi = {10.1016/j.aop.2011.07.007},
journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 9,
volume = 326,
place = {United States},
year = {2011},
month = {9}
}