Journal
PHYSICAL REVIEW B
Volume 102, Issue 20, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.102.201111
Keywords
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Funding
- Deutsche Forschungsgemeinschaft (DFG) [SFB 1143, 247310070]
- Wurzburg-Dresden Cluster of Excellence ct.qmat [EXC 2147, 390858490]
- Emmy Noether program [JA2306/41, 411750675]
- IMPRS for Many Particle Systems in Structured Environment at MPI-PKS
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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.
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