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We solve the spin-1 quantum Ising model with single-ion anisotropy by mappingit onto a series of segmented spin-1/2 transverse Ising chains, separated bythe $S^z =0$ states called holes. A recursion formula is derived for thepartition function to simplify the summation of hole configurations. Thisallows the thermodynamic quantities of this model to be rigorously determinedin the thermodynamic limit. The low temperature behavior is governed by theinterplay between the hole excitations and the fermionic excitations withineach spin-1/2 Ising segment. The quantum critical fluctuations around the Isingcritical point of the transverse Ising model are strongly suppressed by thehole excitations.

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