An Anyon Model in a Toric Honeycomb Lattice
Abstract
We study an anyon model in a toric honeycomb lattice. The ground states and the low-lying excitations coincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics. This model is helpful to understand the toric code of anyons in a more symmetric way. On the other hand, there is a direct relation between this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan—Wigner transformation. We discuss the equivalence between these two models in the low-lying sector and realize these anyon excitations in a conventional fermion system. The analysis for the ground state degeneracy in the last section can also be thought of as a complementarity of our previous work [Phys. A: Math. Theor. 43 (2010) 105306].
- Publication:
-
Communications in Theoretical Physics
- Pub Date:
- January 2011
- DOI:
- 10.1088/0253-6102/55/1/16
- arXiv:
- arXiv:1006.0804
- Bibcode:
- 2011CoTPh..55...80L
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- 5 pages, 3 figures