Explicit demonstration of nonabelian anyon, braiding matrix and fusion rules in the Kitaev-type spin honeycomb lattice models

Details Explicit demonstration of nonabelian anyon, braiding matrix and fusion rules in the Kitaev-type spin honeycomb lattice models Explicit demonstration of nonabelian anyon, braiding matrix and fusion rules in the Kitaev-type spin honeycomb lattice models

2008-04-03

arxiv.org/abs/0804.0483v3

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures; references added; some discussions on the A phase added; derivations to the fusion rules and braiding matr

Scientific paper

The exact solubility of the Kitaev-type spin honeycomb lattice model was proved by means of a Majorana fermion representation or a Jordan-Wigner transformation while the explicit form of the anyon in terms of Pauli matrices became not transparent. The nonabelian statistics of anyons and the fusion rules can only be expressed in indirect ways to Pauli matrices. We convert the ground state and anyonic excitations back to the forms of Pauli matrices and explicitly demonstrate the nonabelian anyonic statistics as well as the fusion rules. These results may instruct the experimental realization of the nonabelian anyons. We suggest a proof-in-principle experiment to verify the existence of the nonabelian anyons in nature.

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