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

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