2020/05/31 by Sreejith Chulliparambil, Urban F. P. Seifert, Matthias Vojta +2
Physics and Astronomy · #Advanced Condensed Matter Physics #Anyon #Fermion #Gauge theory #MAJORANA #Majorana fermion #Order (exchange) #Parity (physics) #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Quasiparticle #Superconductivity #Theoretical physics #Topological Materials and Phenomena #Topological quantum computer #cond-mat.str-el #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevb.102.201111
published as Phys. Rev. B 102, 201111 (2020) · 6+9 pages, 2+1 figures, published version
arxiv created 2020/11/11 · openalex publication_date 2020/11/11 · arxiv updated 2020/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In two dimensions, the topological order described by ℤ2 gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chern number \ensuremathν is classified by \ensuremathν\phantom\rule0.28em0exmod\phantom\rule0.28em0ex16 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 \mathrm\ensuremathΓ matrices satisfying the Clifford algebra, enjoy a global SO(\ensuremathν) symmetry, and live on either square or honeycomb lattices depending on the parity of \ensuremathν. 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 \ensuremathν=2 and \ensuremathν=3 models to materials with Kugel-Khomskii-type spin-orbital interactions is discussed.