Magnetization process and updated phase diagram of one-dimensional S=1 Ising model with single-ion anisotropy under magnetic field

•Detailed magnetizatic structures of the whole phase diagram are uncovered.•Two novel phases with the same magnetization plateau are distinguished.•An updated ground-state phase diagram is proposed.•All the states are shown to be direct matrix product states.•Fidelity per site can be used to describe these first-order QPTs well.

By the infinite time-evolving block decimation (iTEBD) technique, the magnetization process in spin-1 Ising model with single-ion anisotropy under external field is investigated in the thermodynamic limit. An updated phase diagram is proposed, and the detailed magnetic structures of the phase diagram are uncovered. It must be noted that two interesting phases with same magnetization plateau (Mz=0) but different magnetic structures are distinguished. Furthermore, they are verified to be an ideal Néel phase and an ideal large-D phase respectively. In addition, a first-order quantum phase transition line between them is determined to be at D=1.