From String Nets to Nonabelions
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 lowenergy subspace of a model of quantum spins on a lattice with shortranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for its ground state and lowlying quasiparticle excitations to be in the DFib topological phase. 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2006
 arXiv:
 arXiv:condmat/0610583
 Bibcode:
 2006cond.mat.10583F
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 13 pages