Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model
Yan-Wei Dai(代艳伟)1,†, Ai-Min Chen(陈爱民)2,‡, Xi-Jing Liu(刘希婧)3, and Yao-Heng Su(苏耀恒)2
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
Abstract 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.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11805285), the Natural Science Foundation of Shaanxi Province of China (Grant No. 2022JM-033), and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN 201900703).
Yan-Wei Dai(代艳伟), Ai-Min Chen(陈爱民), Xi-Jing Liu(刘希婧), and Yao-Heng Su(苏耀恒) Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model 2023 Chin. Phys. B 32 090304
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