Entanglement spectrum and quantum phase transitions in one-dimensional S ¼ 1 XXZ model with uniaxial single-ion anisotropy

Guang-Hua Liu a,n , Wei Li b , Wen-Long You c , Gang Su b , Guang-Shan Tian d a Department of Physics, Tianjin Polytechnic University, Tianjin 300387, China b Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, College of Physical Sciences, University of Chinese Academy of Sciences, P. O. Box 4588, Beijing 100049, China c School of Physical Science and Technology, Soochow University, Suzhou, Jiangsu 215006, China d School of Physics, Peking University, Beijing 100871, China

Quantum phase transitions (QPTs) in one-dimensional S ¼ 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.