Anyons in an exactly solved model and beyond
- California Institute of Technology, Pasadena, CA 91125 (United States)
A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z{sub 2} gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number {nu}. The Abelian and non-Abelian phases of the original model correspond to {nu}=0 and {nu}=+/-1, respectively. The anyonic properties of excitation depend on {nu} mod 16, whereas {nu} itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.
- OSTI ID:
- 20766977
- Journal Information:
- Annals of Physics (New York), Vol. 321, Issue 1; Other Information: DOI: 10.1016/j.aop.2005.10.005; PII: S0003-4916(05)00238-1; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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