Exact results of a dimerized S=1 Ising chain with single-ion anisotropy

The dimerized spin-1 Ising chain with both longitude and transverse single-ion anisotropies Dz and Dx   is solved exactly by means of a mapping to the spin-12 Ising chain with the alternating transverse fields and the Jordan–Wigner transformation. The analytical expressions of the quasi-particles’ spectra Λk, the minimal energy gap Δ0 for exciting a fermion quasi-particle, the minimal energy gap Δh for exciting a hole, and the ground-state energy Eg are obtained. The phase diagram of the ground state is also given. The results show that the system exhibits a series of quantum phase transitions depending on the dimerization strength of the crystal fields, while the quantum critical points are determined exactly.