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

Abstract

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 J 1, J 2, D x and D z . We obtain the quasi-particles' spectra Λ k , the dimerization gap Δ d , the minimal energy Δ 0 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 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.