Friday, July 27, 2012

1207.6169 (Ling-Yan Hung et al.)

String-Net Models with $Z_N$ Fusion Algebra    [PDF]

Ling-Yan Hung, Yidun Wan
We study the Levin-Wen string-net model with a $\Z_N$ type fusion algebra. Solutions of the local constraints of this model correspond to $Z_N$ gauge theory and double Chern-simons theories with quantum groups. For the first time, we explicitly construct a spin-$(N-1)/2$ model with $\Z_N$ gauge symmetry on a triangular lattice as an exact dual model of the string-net model with a $\Z_N$ type fusion algebra on a honeycomb lattice. This exact duality exists only when the spins are coupled to a $\Z_N$ gauge field living on the links of the triangular lattice. The ungauged $\Z_N$ lattice spin models are a class of quantum systems that bear symmetry-protected topological phases that may be classified by the third cohomology group $H^3(\Z_N,U(1))$ of $\Z_N$. Our results apply also to any case where the fusion algebra is identified with a finite group algebra or a quantusm group algebra.
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