Rigorous Solution of the Spin-1 Quantum Ising Model with Single-ion Anisotropy

We solve the spin-1 quantum Ising model with single-ion anisotropy by mapping it onto a series of segmented spin-1/2 transverse Ising chains, separated by the $S^z =0$ states called holes. A recursion formula is derived for the partition function to simplify the summation of hole configurations. This allows the thermodynamic quantities of this model to be rigorously determined in the thermodynamic limit. The low temperature behavior is governed by the interplay between the hole excitations and the fermionic excitations within each spin-1/2 Ising segment. The quantum critical fluctuations around the Ising critical point of the transverse Ising model are strongly suppressed by the hole excitations.