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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 |
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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.
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Received: 15 September 2022
Revised: 17 November 2022
Accepted manuscript online: 16 December 2022
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PACS:
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03.67.-a
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(Quantum information)
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03.67.Mn
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(Entanglement measures, witnesses, and other characterizations)
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05.70.Fh
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(Phase transitions: general studies)
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75.40.Mg
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(Numerical simulation studies)
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| 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). |
Corresponding Authors:
Yan-Wei Dai, Ai-Min Chen
E-mail: daiyw@cqu.edu.cn;chenaimin_xa@163.com
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Cite this article:
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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