From String Nets to Nonabelions |
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| Authors: | Lukasz Fidkowski Michael Freedman Chetan Nayak Kevin Walker and Zhenghan Wang |
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| Institution: | (1) Microsoft Station Q, University of California, Santa Barbara, 93106-6105, USA;(2) Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547, USA;(3) Department of Mathematics, Indiana University, Bloomington, IN 47405, USA;(4) Department of Physics, Stanford University, Stanford, CA 94305, USA |
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| 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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