Exact solutions of a class of S=1 quantum Ising spin models

We propose a hole decomposition scheme to exactly solve a class of spin-1 quantum Ising models with transverse or longitudinal single-ion anisotropy. In this scheme, the spin-1 model is mapped onto a family of the S=1/2 transverse Ising models, characterized by the total number of holes. A recursion formula is derived for the partition function based on the reduced S=1/2 Ising model. This simplifies greatly the summation over all the hole configurations. It allows the thermodynamic quantities to be rigorously determined in the thermodynamic limit. The ground-state phase diagram is determined for both the uniform and dimerized spin chains. The corresponding thermodynamic properties are calculated and discussed.