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 D(z) and D(x) is solved exactly by means of a mapping to the spin-1/2 Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles' spectra Lambda(k), the minimal energy gap Delta(0) for exciting a fermion quasi-particle , the minimal energy gap Delta(h) for exciting a hole, and the ground-state energy E(g) 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. (C) 2009 Elsevier B.V. All rights reserved.