Communications in Mathematical Physics

, Volume 287, Issue 3, pp 805–827 | Cite as

From String Nets to Nonabelions

  • Lukasz Fidkowski
  • Michael Freedman
  • Chetan Nayak
  • Kevin Walker
  • Zhenghan Wang
Open Access
Article

Abstract

We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for the system to be in the DFib (Doubled Fibonacci) topological phase, that is, be described at low energy by an SO(3)3 × SO(3)3 doubled Chern-Simons theory, with the appropriate non-abelian statistics governing the braiding of the low-lying quasiparticle excitations (nonabelions). Using the string net wavefunction, we describe the properties of this phase. Our discussion is informed by mappings of string net wavefunctions to the chromatic polynomial and the Potts model.

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Lukasz Fidkowski
    • 1
    • 4
  • Michael Freedman
    • 1
  • Chetan Nayak
    • 1
    • 2
  • Kevin Walker
    • 1
  • Zhenghan Wang
    • 1
    • 3
  1. 1.Microsoft Station QUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of Physics and AstronomyUniversity of CaliforniaLos AngelesUSA
  3. 3.Department of MathematicsIndiana UniversityBloomingtonUSA
  4. 4.Department of PhysicsStanford UniversityStanfordUSA

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