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 single-ion 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 J₁, J₂, D_x and D_z. We obtain the quasi-particles' spectra Λ_k, the dimerization gap Δ_d, the minimal energy Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δ_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 J₁ and J₂ 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.