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

doi:10.1088/1674-1056/acac0c

中国物理B ›› 2023, Vol. 32 ›› Issue (9): 90304-090304.doi: 10.1088/1674-1056/acac0c

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

收稿日期:2022-09-15 修回日期:2022-11-17 接受日期:2022-12-16 发布日期:2023-08-23
通讯作者: Yan-Wei Dai, Ai-Min Chen E-mail:daiyw@cqu.edu.cn;chenaimin_xa@163.com
基金资助:
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).

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

Received:2022-09-15 Revised:2022-11-17 Accepted:2022-12-16 Published:2023-08-23
Contact: Yan-Wei Dai, Ai-Min Chen E-mail:daiyw@cqu.edu.cn;chenaimin_xa@163.com
Supported by:
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).

摘要/Abstract

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

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.

Key words: commensurate and incommensurate phases, symmetry-protected topological phase, transversal spin correlation

中图分类号: (Quantum information)

03.67.-a

03.67.Mn (Entanglement measures, witnesses, and other characterizations) 05.70.Fh (Phase transitions: general studies) 75.40.Mg (Numerical simulation studies)

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[J]. 中国物理B, 2023, 32(9): 90304-090304.

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[J]. Chin. Phys. B, 2023, 32(9): 90304-090304.

参考文献

[1] Sachdev S 1999 Quantum Phase Transitions (Cambridge University Press, Cambridge)
[2] Haldane F D M 1983 Phys. Rev. Lett. 50 1153
[3] Haldane F D M 1983 Phys. Lett. A 93 464
[4] Murashima T and Nomura K 2006 Phys. Rev. B 73 214431
[5] Fáth G and Sütõ A 2000 Phys. Rev. B 62 3778
[6] Nomura K 2003 J. Phys. Soc. Jpn. 72 476
[7] Yarotsky D A 2008 J. Stat. Phys. 130 957
[8] Chubukov A V 1991 Phys. Rev. B 43 3337
[9] Kawashima N 2002 Prog. Theor. Phys. Suppl. 145 138
[10] Ivanov B A and Kolezhuk A K 2003 Phys. Rev. B 68 052401
[11] Buchta K, Fáth G, Legeza O and Sólyom J 2005 Phys. Rev. B 72 054433
[12] Rizzi M, Rossini D, De Chiara G, Montangero S and Fazio R 2005 Phys. Rev. Lett. 95 240404
[13] Läuchli A, Schmid G and Trebst S 2006 Phys. Rev. B 74 144426
[14] Porras D, Verstraete F and Cirac J I 2006 Phys. Rev. B 73 014410
[15] Romero-Isart O, Eckert K and Sanpera A 2007 Phys. Rev. A 75 050303
[16] Dai Y W, Shi Q Q, Zhou H Q and McCulloch I 2022 arXiv: 2201.01434
[17] Chen A M, Su Y H and Wang H L 2015 Eur. Phys. J. B 88 269
[18] Jakab D, Szirmai G and Zimborás Z 2018 J. Phys. A: Math. Theor. 51 105201
[19] Li P and Kou S P 2012 J. Phys.: Condens. Matter 24 446001
[20] Fáth G and Sólyom J 1991 Phys. Rev. B 44 11836
[21] Sutherland B 1975 Phys. Rev. B 12 3795
[22] Batista C D, Ortiz G and Gubernatis J E 2002 Phys. Rev. B 65 180402
[23] Affleck I 1990 J. Phys.: Condens. Matter 2 405
[24] Takhtajan L 1982 Phys. Lett. A 87 479
[25] Babujian H 1983 Nucl. Phys. B 215 317
[26] Barber M N and Batchelor M T 1989 Phys. Rev. B 40 4621
[27] Affeck T, Kennedy T, Lieb E and Tasaki H 1987 Phys. Rev. Lett. 59 799
[28] Pollmann F, Turner A M, Berg E and Oshikawa M 2010 Phys. Rev. B 81 064439
[29] Chen X, Gu Z C and Wen X G 2011 Phys. Rev. B 83 035107
[30] Pollmann F, Turner A M, Berg E and Oshikawa M 2010 Phys. Rev. B 81 064439
[31] Rao W J, Zhu G Y and Zhang G M 2016 Phys. Rev. B 93 165135
[32] Vidal G 2007 Phys. Rev. Lett. 98 070201
[33] Li H and Haldane F D M 2008 Phys. Rev. Lett. 101 010504
[34] Levin M and Wen X G 2006 Phys. Rev. Lett. 96 110405
[35] Kitaev A and Preskill J 2006 Phys. Rev. Lett. 96 110404
[36] Pollmann F and Turner A M 2010 Phys. Rev. B 81 064439
[37] Calabrese P and Lefevre A 2008 Phys. Rev. A 78 032329
[38] McCulloch I P 2008 arXiv: 0804.2509
[39] Pollmann F and Turner A M 2012 Phys. Rev. B 86 125441
[40] Fuji Y, Pollmann F and Oshikawa M 2015 Phys. Rev. Lett. 114 177204
[41] Kennedy T and Tasaki H 1992 Phys. Rev. B 45 304
[42] Tu H H, Zhang G M and Xiang T 2008 J. Phys. A: Math. Theor. 41 415201
[43] White S R and Huse D A 1993 Phys. Rev. B 48 3844
[44] Sengupta P and Batista C D 2007 Phys. Rev. Lett. 98 227201
[45] Zare M H and Mosadeq H 2021 Phys. Rev. B 104 115154
[46] Dai Y W, Liu X J, Li S H and Chen A M 2022 Phys. Rev. E 106 054104

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

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

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Chi Zhang(张驰), Tian-Le Wang(王天乐), Ze-An Zhao(赵泽安), Xiao-Yan Yang(杨小燕), Liang-Liang Guo(郭亮亮), Zhi-Long Jia(贾志龙), Peng Duan(段鹏), and Guo-Ping Guo(郭国平). Fast and perfect state transfer in superconducting circuit with tunable coupler[J]. 中国物理B, 2023, 32(11): 110305-110305.
[2]	Si-Yuan Liu(刘思远) and Heng Fan(范桁). The application of quantum coherence as a resource[J]. 中国物理B, 2023, 32(11): 110304-110304.
[3]	Liu-Yong Cheng(程留永), Shi-Feng Zhang(张世凤), Zuan Meng(孟钻), Hong-Fu Wang(王洪福), and Shou Zhang(张寿). Deterministic remote preparation of multi-qubit equatorial states through dissipative channels[J]. 中国物理B, 2023, 32(11): 110307-110307.
[4]	Huan Yang(杨欢), Ling-Ling Xing(邢玲玲), Ming-Ming Du(杜明明), Min Kong(孔敏), Gang Zhang(张刚), and Liu Ye(叶柳). Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame[J]. 中国物理B, 2023, 32(10): 100305-100305.
[5]	Meng-Jun Hu(胡孟军) and Yong-Sheng Zhang(张永生). Digital holographic imaging via direct quantum wavefunction reconstruction[J]. 中国物理B, 2023, 32(10): 100312-100312.
[6]	Zhimin Wang(王治旻), Zhuang Ma(马壮), Xiangmin Yu(喻祥敏), Wen Zheng(郑文), Kun Zhou(周坤), Yujia Zhang(张宇佳), Yu Zhang(张钰), Dong Lan(兰栋), Jie Zhao(赵杰), Xinsheng Tan(谭新生), Shaoxiong Li(李邵雄), and Yang Yu(于扬). Realization of high-fidelity and robust geometric gates with time-optimal control technique in superconducting quantum circuit[J]. 中国物理B, 2023, 32(10): 100304-100304.
[7]	Hao Wu(吴昊), Hang Zhang(张航), Yiwu Zhu(朱益武), Gaofeng Luo(罗高峰), Zhiyue Zuo(左峙岳), Xinchao Ruan(阮新朝), and Ying Guo(郭迎). Non-Gaussian approach: Withstanding loss and noise of multi-scattering underwater channel for continuous-variable quantum teleportation[J]. 中国物理B, 2023, 32(10): 100311-100311.
[8]	Rozhin Yousefjani, Xingjian He(何行健), and Abolfazl Bayat. Long-range interacting Stark many-body probes with super-Heisenberg precision[J]. 中国物理B, 2023, 32(10): 100313-100313.
[9]	Si-Wu Li(李思吾), Tianfeng Feng(冯田峰), Xiao-Long Hu(胡骁龙), and Xiaoqi Zhou(周晓祺). State transfer and entanglement between two- and four-level atoms in a cavity[J]. 中国物理B, 2023, 32(10): 104214-104214.
[10]	Chunhe Xiong(熊春河), Wentao Qi(齐文韬), Maoke Miao(缪茂可), and Minghui Wu(吴明晖). Geometric discord of tripartite quantum systems[J]. 中国物理B, 2023, 32(10): 100301-100301.
[11]	Chen-Yi Huang(黄晨猗) and Shi-Bin Zhang(张仕斌). A backdoor attack against quantum neural networks with limited information[J]. 中国物理B, 2023, 32(10): 100306-100306.
[12]	Ying-Jie Qu(曲英杰), Zhao Chen(陈钊), Wei-Jie Wang(王伟杰), and Hong-Yang Ma(马鸿洋). Approximate error correction scheme for three-dimensional surface codes based reinforcement learning[J]. 中国物理B, 2023, 32(10): 100307-100307.
[13]	Xin Xu(徐鑫) and Ai-Han Yin(殷爱菡). Quantum homomorphic broadcast multi-signature based on homomorphic aggregation[J]. 中国物理B, 2023, 32(7): 70302-070302.
[14]	Jinge Yan(颜金歌), Lili Yan(闫丽丽), and Shibin Zhang(张仕斌). A new method of constructing adversarial examples for quantum variational circuits[J]. 中国物理B, 2023, 32(7): 70304-070304.
[15]	Lei-Xin Wu(伍磊鑫), Yan-Yan Feng(冯艳艳), and Jian Zhou(周健). Improving source-in-the-middle continuous-variable quantum key distribution using a heralded hybrid linear amplifier[J]. 中国物理B, 2023, 32(7): 70310-070310.