Entanglement spectrum and quantum phase transitions in one-dimensional S=1 XXZ model with uniaxial single-ion anisotropy

Quantum phase transitions (QPTs) in one-dimensional S=1 XXZ model with uniaxial single-ion anisotropy are investigated. Bipartite entanglement, entanglement spectrum, and Schmidt gap are found to be capable of describing all the QPTs, even the infinite-order Berezinskii-Kosterlitz-Thouless (BKT) transition. According to the singular behavior of the second-order derivative of ground-state energy, the QPT between XY2 and antiferromagnetic phases is a second-order but not a BKT transition. Energy level crossing, accompanied with discontinuous entanglement entropy and entanglement spectrum, is observed at the transition point between the large-D and antiferromagnetic phases, therefore it should be a first-order QPT. In addition, doubly degenerate entanglement spectrum in the Haldane phase is observed.