Exact results of an alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse singleion anisotropies are solved exactly by means of a mapping of the spin-1/2 transverse Ising chain and the Jordan-Wigner transformation. The ground state quantities are strongly dependent on the model Hamiltonian parameters J(1), J(2), D(x) and D(z). We obtain the quasi-particles' spectra A(k), the dimerization gap Delta(d), the minimal energy Delta(0) for exciting a fermion quasi-particle, the minimal energy Delta(h) for exciting a hole and the ground state energy E(g). The phase diagram of the ground state is also given. The results show that the alternating bond just quantitatively changes the ground state properties; no matter the nearest-neighbor exchange interactions J(1) and J(2) are equal or not, when D(z) >= 0 for any finite value of D(x) there is no quantum critical point and the ground state is always in a spin ordered phase. (C) 2011 Elsevier B.V. All rights reserved.