Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model  

作　　者：代艳伟 陈爱民 刘希婧 苏耀恒 Yan-Wei Dai;Ai-Min Chen;Xi-Jing Liu;Yao-Heng Su(Centre for Modern Physics and Department of Physics,Chongqing University,Chongqing 400044,China;School of Science,Xi'an Polytechnic University,Xi'an 710048,China;The School of Materials Science and Engineering,Chongqing Jiaotong University,Chongqing 400044,China)

机构地区：[1]Centre for Modern Physics and Department of Physics,Chongqing University,Chongqing 400044,China [2]School of Science,Xi'an Polytechnic University,Xi'an 710048,China [3]The School of Materials Science and Engineering,Chongqing Jiaotong University,Chongqing 400044,China

出　　处：《Chinese Physics B》2023年第9期157-162,共6页中国物理B（英文版）

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)。

摘　　要：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.

关 键 词：commensurate and incommensurate phases symmetry-protected topological phase transversal spin correlation 

分 类 号：O469[理学—凝聚态物理]