From string nets to nonabelions

Lukasz Fidkowski, Michael Freedman, Chetan Nayak, Kevin Walker, Zhenghan Wang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)805-827
Number of pages23
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - May 2009
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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