Celebratio Mathematica — Freedman

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article L. Fidkowski, M. Freedman, C. Nayak, K. Walker, and Z. Wang: “From string nets to nonabelions,” Comm. Math. Phys. 287 : 3 (2009), pp. 805–827. MR 2486662 Zbl 1196.82072 ArXiv cond-mat/0610583

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 \( \mathit{SO}(3)_3\times\mathit{SO}(3)_3 \) 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.

Zhenghan Wang	Related
Lukasz Fidkowski	Related
Kevin Walker	Related
Chetan Nayak	Related