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This is a supplementary material of our recent paper\cite{yangPRB}, where aclass of exactly solvable S=1 quantum Ising spin models were studied based onthe hole decomposition scheme. Here we provide some details for the Greenfunctions, the spin-spin correlation functions, as well as the spinsusceptibility in the presence of dimerization.

Green functions and correlation functions of a solvable S=1 quantum Ising spin model with dimerization