2015/08/06 by Miguel Jorge Bernabé Ferreira, Miguel Jorge Bernabe Ferreira, Ferreira, Miguel Jorge Bernabe +4 · 1 citation
Mathematics · Physics and Astronomy · #Anyon #Combinatorics #Condensed matter physics #Fibonacci number #Geometry #Hamiltonian (control theory) #Homogeneous space #Ising model #Lattice (music) #Mathematical physics #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum chaos and dynamical systems #Quantum computer #Quantum many-body systems #Quantum mechanics #Theoretical and Computational Physics #Theoretical physics #Topological Materials and Phenomena #Topological quantum computer #Toric code #cond-mat.str-el #hep-th
paper · pdf · doi:10.48550/arxiv.1508.01399
published in arXiv (Cornell University) (Cornell University) · 8 pages, 5 figures. All the Abelian cases are covered
openalex publication_date 2015/08/06 · arxiv created 2015/12/10 · arxiv updated 2015/12/14 · openalex created_date 2023/02/28 · openalex updated_date 2026/07/28
The global e-m exchange symmetry of the toric code is realized locally\nthrough an exactly solvable Hamiltonian on a two dimensional lattice which has\nno lattice dislocations and their associated defect line. The Hamiltonian is\nstill changed locally in selected sites where we wish to realize this anyon\nsymmetry. We refer to these selected sites as defect sites in analogy with the\nusual lattice defects. The operators on the defect sites condense dyons of the\ntoric code and are shown to support states which obey the fusion rules of Ising\nanyons just as the lattice dislocations thus achieving the transition to the\nIsing phase from the toric code phase. They can also be introduced in an entire\nregion leading to an idea of non-localized defects. The method leads to a\nnatural generalization for other Abelian groups where they help realize all the\nanyon exchange symmetries locally.\n