2016/08/31 by Carlos Fernandez-Gonzalez, Carlos García-Gutiérrez Fernández, Roger S. K. Mong +4
Computer Science · Mathematics · Physics and Astronomy · #Abelian group #Anyon #Combinatorics #Condensed matter physics #Formalism (music) #Mathematical physics #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Spins #Symmetrization #Theoretical physics #Topological order #Topological quantum computer #Toric code #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.94.155106
published as Phys. Rev. B 94, 155106 (2016) · 10 pages. v2: accepted version
arxiv created 2016/09/29 · openalex publication_date 2016/10/05 · arxiv updated 2016/10/06 · openalex created_date 2016/11/30 · openalex updated_date 2026/08/06
Symmetrization of topologically ordered wave functions is a powerful method for constructing new topological models. Here we study wave functions obtained by symmetrizing quantum double models of a group G in the projected entangled pair states (PEPS) formalism. We show that symmetrization naturally gives rise to a larger symmetry group \stackrel\ifmmode \else \~\fiG which is always non-Abelian. We prove that by symmetrizing on sufficiently large blocks, one can always construct wave functions in the same phase as the double model of \stackrel\ifmmode \else \~\fiG. In order to understand the effect of symmetrization on smaller patches, we carry out numerical studies for the toric code model, where we find strong evidence that symmetrizing on individual spins gives rise to a critical model which is at the phase transitions of two inequivalent toric codes, obtained by anyon condensation from the double model of \stackrel\ifmmode \else \~\fiG.