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arXiv · 1711.07149

Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice

Zhao-Yang Dong·Shun-Li Yu·Jian-Xin Li
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Abstract

To study exotic excitations described by parafermions in the possible spin liquid states of SU($n$) spin systems, we introduce a parafermion parton approach. The SU($n$) spin operators can be represented by clock and shift matrices, which are shown to be the polynomials of parafermion operators in the parafermion representation. We find that SU($n$) spins can be decomposed into $n$ parafermion matrices of degree one. In this decomposition, the spin has a $\{\bigotimes{\rm SU}(n)\}^{n-1}$ gauge symmetry. As an application, we study the one-dimensional three-state clock model and generalized Kitaev model by a mean-field theory, both of them have been proved to be related to parafermion excitations. We find that with the symmetries of translations, $6$-fold rotation and combination of parity and time reversal, there are $9$ types and $102$ solutions for two-dimensional $Z_3$ parafermion spin liquids on the honeycomb lattice. On the contrast, there are $9$ types and $36$ solutions if both parity and time-reversal symmetries are present. Our results provide a novel route for the systematic search of new types of spin liquids with exotic anyon excitations.

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Zhao-Yang Dong, Shun-Li Yu, Jian-Xin Li. 2017-11-20. Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice. https://doi.org/10.1103/physrevb.96.245114

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