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arXiv · 2005.13683

Microscopic models for Kitaev's sixteenfold way of anyon theories

Sreejith Chulliparambil·Urban F. P. Seifert·Matthias Vojta·Lukas Janssen·Hong-Hao Tu
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Abstract

In two dimensions, the topological order described by $\mathbb{Z}_2$ gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chern number $ν$ is classified by $ν\; \mathrm{mod}\; 16$ as predicted by Kitaev [Ann. Phys. 321, 2 (2006)]. 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 $Γ$ matrices satisfying the Clifford algebra, enjoy a global $\mathrm{SO}(ν)$ symmetry, and live on either square or honeycomb lattices depending on the parity of $ν$. 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 $ν=2$ and $ν=3$ models to materials with Kugel-Khomskii-type spin-orbital interactions is discussed.

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Sreejith Chulliparambil, Urban F. P. Seifert, Matthias Vojta, Lukas Janssen, Hong-Hao Tu. 2020-11-11. Microscopic models for Kitaev's sixteenfold way of anyon theories. https://doi.org/10.1103/physrevb.102.201111

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