Magnetization process and quantum entanglement in spin-1 XXZ model with single-ion anisotropy under external field

By the infinite time-evolving block decimation (iTEBD) technique, the magnetization process and the quantum phase transitions (QPTs) in the spin-1 XXZ model with single-ion anisotropy under external field are investigated. It is found that, all the phases will be destroyed by a sufficient strong magnetic field. Before they come into the ferromagnetic (fully polarized) phase, some interesting intermediate phases are induced. A pseudo order Oixy=〈Six〉2+〈Siy〉2 with finite truncation dimension χ can be used to describe the XY1 phase. Especially, the Oxyi with finite χ is found to be nonzero in the XY1 phase, but vanishes in the XY2 phase. It means that two kinds of XY phases can be distinguished by the pseudo order parameter Oxyi. All the QPTs can be described by the behavior of the entanglement entropy and the ground-state energy. QPTs from the XY phase to the large-D, Haldane, and antiferromagnetic phases are found to be infinite-order BKT type transitions, but the QPTs from the XY1 phase to the ferromagnetic phase and XY2 have second-order characters. In addition, doubly degenerate entanglement spectra are observed in the Haldane phase.