%0 Journal Article %1 PhysRevB.102.201111 %A Chulliparambil, Sreejith %A Seifert, Urban F. P. %A Vojta, Matthias %A Janssen, Lukas %A Tu, Hong-Hao %D 2020 %I American Physical Society %J Phys. Rev. B %K b %N 20 %P 201111 %R 10.1103/PhysRevB.102.201111 %T Microscopic models for Kitaev's sixteenfold way of anyon theories %U https://link.aps.org/doi/10.1103/PhysRevB.102.201111 %V 102 %X In two dimensions, the topological order described by $Z_2$ gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chern number $\nu$ is classified by $\; mod\; 16$ 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 $\Gamma$ 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.

@article{PhysRevB.102.201111, abstract = {In two dimensions, the topological order described by $Z_2$ gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chern number $\nu$ is classified by $\; mod\; 16$ 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 $\Gamma$ 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.}, added-at = {2020-12-28T17:44:32.000+0100}, author = {Chulliparambil, Sreejith and Seifert, Urban F. P. and Vojta, Matthias and Janssen, Lukas and Tu, Hong-Hao}, biburl = {https://www.bibsonomy.org/bibtex/2f3624c8c7f8303da8bc5a5c33b3fa3e5/ctqmat}, day = 11, description = {Phys. Rev. B 102, 201111(R) (2020) - Microscopic models for Kitaev's sixteenfold way of anyon theories}, doi = {10.1103/PhysRevB.102.201111}, interhash = {7b526a6603bdadd933f7a2e6e5ec07e8}, intrahash = {f3624c8c7f8303da8bc5a5c33b3fa3e5}, journal = {Phys. Rev. B}, keywords = {b}, month = {11}, note = {cite arxiv:2005.13683Comment: 6+9 pages, 2+1 figures}, number = 20, numpages = {5}, pages = 201111, publisher = {American Physical Society}, timestamp = {2023-10-13T12:51:31.000+0200}, title = {Microscopic models for Kitaev's sixteenfold way of anyon theories}, url = {https://link.aps.org/doi/10.1103/PhysRevB.102.201111}, volume = 102, year = 2020 }