From String Nets to Nonabelions

Details From String Nets to Nonabelions From String Nets to Nonabelions

2006-10-20

arxiv.org/abs/cond-mat/0610583v1

Physics

Condensed Matter

Strongly Correlated Electrons

13 pages

Scientific paper

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 its ground state and low-lying 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.

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