Realization of the exactly solvable Kitaev honeycomb lattice model in a spin-rotation-invariant system

Citation Wang, Fa. " Realization of the exactly solvable Kitaev honeycomb lattice model in a spin-rotation-invariant system. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. The exactly solvable Kitaev honeycomb lattice model is realized as the low-energy effect Hamiltonian of a spin-1/2 model with spin rotation and time-reversal symmetry. The mapping to low-energy effective Hamil-tonian is exact without truncation errors in traditional perturbation series expansions. This model consists of a honeycomb lattice of clusters of four spin-1/2 moments and contains short-range interactions up to six-spin ͑or eight-spin͒ terms. The spin in the Kitaev model is represented not as these spin-1/2 moments but as pseudospin of the two-dimensional spin-singlet sector of the four antiferromagnetically coupled spin-1/2 moments within each cluster. Spin correlations in the Kitaev model are mapped to dimer correlations or spin-chirality correlations in this model. This exact construction is quite general and can be used to make other interesting spin-1/2 models from spin-rotation invariant Hamiltonians. We discuss two possible routes to generate the high-order spin interactions from more natural couplings, which involves perturbative expansions thus breaks the exact mapping, although in a controlled manner.