$Z_3$ generalization of the Kitaev's spin-1/2 model

Abstract

We generalize the Kitaev's spin-1/2 model on the honeycomb by introducing a two-dimensional $Z_3$ clock model on the triangular lattice with three body interaction. We discuss various properties of this model and show that the low energy theory of the $Z_3$ generalized Kitaev model (GKM) is described by a single $Z_3$ parafermion per lattice site coupled to a $Z_3$ gauge field. We also introduce a slave-fermion approach for this GKM, treat the resulting fermionic Hamiltonian at the mean-field level, solve the mean field parameters self-consistently, and obtain the low energy effective Chern-Simons (CS) gauge theory. The resulting CS gauge theory is identical to that of a (221) fractional quantum Hall state. We then go beyond the mean-field approximation and demonstrate that fluctuations generate a uniform interlayer pairing for the dual (221) bilayer state. We argue that this perturbed system can undergo a phase transition to the Fibonacci phase by tuning the interlayer pairing strength.

Accepted for publication in Phys. Rev. B (2014)

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• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Generalized Kitaev Models and Slave Genons
• General phase spaces: from discrete variables to rotor and continuum limits
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Hyperbolic Spin Liquids
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice