Exact results of a mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies DzDz and DxDx 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 ΛkΛk, the minimal energy gap Δ0Δ0 for exciting a fermion quasi-particle, the minimal energy gap ΔhΔh for exciting a hole, and the ground state energy are obtained. The phase diagram of the ground state is also given. The results show that when Dz⩾0Dz⩾0 for any finite value of DxDx, there is no quantum critical point and the ground state is always in a spin ordered phase disregard of the boundary condition in the present system.