Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point...Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point between the two phases.In both phases,the entanglement spectrum shows double degeneracy.We calculate the nonlocal order parameter of the bond-centered inversion in both phases,which rapidly approaches a saturation value of-1 as the segment length increases.The nonlocal order parameter of the bond-centered inversion with a saturation value-1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase.To distinguish the commensurate and incommensurate Haldane phases,the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed.As a result,the transversal spin correlations exhibit different decay forms in both phases.展开更多
基金the National Natural Science Foundation of China(Grant No.11805285)the Natural Science Foundation of Shaanxi Province of China(Grant No.2022JM-033)the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN 201900703)。
文摘Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point between the two phases.In both phases,the entanglement spectrum shows double degeneracy.We calculate the nonlocal order parameter of the bond-centered inversion in both phases,which rapidly approaches a saturation value of-1 as the segment length increases.The nonlocal order parameter of the bond-centered inversion with a saturation value-1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase.To distinguish the commensurate and incommensurate Haldane phases,the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed.As a result,the transversal spin correlations exhibit different decay forms in both phases.
