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Anyons in an exactly solved model and beyond

Kitaev, Alexei (2006) Anyons in an exactly solved model and beyond. Annals of Physics, 321 (1). pp. 2-111. ISSN 0003-4916. doi:10.1016/j.aop.2005.10.005.

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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 Z2 source 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 ν. The Abelian and non-Abelian phases of the original model correspond to ν = 0 and ν = ±1, respectively. The anyonic properties of excitation depend on ν mod 16, whereas ν 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.

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Additional Information:Author preprint; During the years this work was in progress I received genuine interest and words of encouragement from John Preskill, Michael Freedman, Mikhail Feigelman, Grigory Volovik, and many other people. I thank Andreas Ludwig for having convinced me in the importance of the chiral central charge in the study of topological order. A conversation with Dmitri Ivanov was essential for understanding the difference between non-Abelian anyons and Majorana vortices in two-dimensional p-wave superconductors. I also thank Matthew Fisher, Nicholas Read, and Xiao-Gang Wen for helpful discussions. I am especially grateful to Jean Bellissard who read a preliminary version of the manuscript and made some valuable comments; in particular, he directed me to Ref. [50]. This work was supported in part by the National Science Foundation under Grant No. EIA-0086038 and by the Army Research Office under grant No. W911NF-04-1-0236. Published article: Alexei Kitaev (2006) Anyons in an exactly solved model and beyond. Annals of Physics 321:2-111
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Deposited On:09 Mar 2020 14:56
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