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Microscopic models for Kitaev's sixteenfold way of anyon theories

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Chulliparambil,  Sreejith
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Chulliparambil, S., Seifert, U. F. P., Vojta, M., Janssen, L., & Tu, H.-H. (2020). Microscopic models for Kitaev's sixteenfold way of anyon theories. Physical Review B, 102(20): 201111. doi:10.1103/PhysRevB.102.201111.


Cite as: http://hdl.handle.net/21.11116/0000-0007-F638-5
Abstract
In two dimensions, the topological order described by Z(2) gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chem number nu is classified by nu mod 16 as predicted by Kitaev [Ann. Phys. 321. 2 (20064 Here, we provide a systematic and complete construction of microscopic models realizing this so-called sixteenfold way of anyon theories. These models are defined by Gamma matrices satisfying the Clifford algebra, enjoy a global SO(nu) symmetry, and live on either square or honeycomb lattices depending on the parity of nu. We show that all these models are exactly solvable by using a Majorana representation and characterize the topological order by calculating the topological spin of an anyonic quasiparticle and the ground-state degeneracy. The possible relevance of the nu = 2 and nu = 3 models to materials with Kugel-Khomskii-type spin-orbital interactions is discussed.