2011/01/31 by M. Aguado, Miguel Aguado · 1 citation
Mathematics · Physics and Astronomy · #Abelian group #Advanced Condensed Matter Physics #Hamiltonian (control theory) #Ising model #Lattice (music) #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum computer #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #Theoretical physics #Toric code #Torus #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1016/j.aop.2011.07.007
published as Annals Phys.326:2444-2473,2011 · 46 pages, 25 eps figures
openalex publication_date 2011/07/25 · arxiv created 2011/08/16 · arxiv updated 2011/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.