基于投影纠缠对态算法优化的研究

李生好; 伍小兵; 黄崇富; 王洪雷

doi:10.7498/aps.63.140501

摘要

二维强关联电子量子格点系统的投影纠缠对态（PEPS）算法是数值计算领域中研究二维强关联电子量子格点系统最为重要的张量网络算法. 基于PEPS算法研究二维量子XYX模型与二维量子Ising 模型，本文对PEPS算法进行了一些优化和改进研究，这些优化和改进主要体现在如何进行PEPS张量的更新与如何进行物理观测量的计算这两个方面，从而可以大大提高计算资源的利用. 因而优化和改进后的PEPS算法可为研究热力学极限下的二维强关联电子量子格点系统的量子相变和量子临界现象提供一种更有效的强大的工具.

关键词:

Abstract

In the numerical calculation, the projected entangled pair state (PEPS) algorithm is the most important tensor network algorithm for two-dimensional strongly correlated electron quantum lattice system. In this paper, the optimization of PEPS for two-dimensional quantum system is discussed. An optimization connection between how to update the PEPS tensor and how to calculate the physical observable is investigated, for the tensor network algorithm based on the PEPS representation, which can greatly improve the utilization of computing resources. In this case, optimized PEPS algorithm, as a powerful tool, can be used to study quantum phase transitions and quantum critical phenomena in the thermodynamic limit of the two-dimensional strongly correlated electron quantum lattice system. Of course, optimization of PEPS algorithm program has many other applications, such as adding U(1) and SO(2) symmetry in PEPS algorithm, etc.

Keywords:

作者及机构信息

1.
重庆工程职业技术学院, 重庆 400037;

2.
重庆医科大学基础医学院, 重庆 400016

基金项目: 国家自然科学基金（批准号：11104362）和重庆市教委科学技术研究项目（批准号：KJ1403203）资助的课题.

Authors and contacts

1.
Chongqing Institute of Engineering, Chongqing 400037, China;

2.
Faculty of Basic Medical Science, Chongqing Medical University, Chongqing 400016, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11104362) and the Scientific and Technological Research Program of Chongqing Municipal Education Commission, China (Grant No. KJ1403203).

参考文献

[1]	Wilson K G 1975 Rev. Mod. Phys. 47 773
[2]	Krishnamurthy H R, Wilkins J W, Wilson K G 1980 Phys. Rev. B 21 1044
[3]	Wilson K G 1971 Phys. Rev. B 4 3174
[4]	Wilson K G 1971 Phys. Rev. B 4 3184
[5]	White S R 1992 Phys. Rev. Lett. 69 2863
[6]	White S R 1992 Phys. Rev. B 48 10345
[7]	Ostlund S, Rommer S 1995 Phys. Rev. Lett. 75 3537
[8]	Verstraete F, Porras D, Cirac J I 2004 Phys. Rev. Lett. 93 227205
[9]	Vidal G 2007 Phys. Rev. Lett. 98 070201
[10]	Murg V, Verstraete F, Cirac J I 2007 Phys. Rev. A 75 033605
[11]	Jordan J, Orús R, Vidal G, Verstraete F, Cirac J I 2008 Phys. Rev. Lett. 101 250602
[12]	Vidal G 2007 Phys. Rev. Lett. 99 220405
[13]	Evenbly G, Vidal G 2009 Phys. Rev. B 79 144108
[14]	Zhao J H, Wang H T 2012 Acta Phys. Sin. 61 220502 (in Chinese) [赵建辉, 王海涛 2012 61 220502]
[15]	Shi Q Q, Li S H, Zhao J H, Zhou H Q 2009 arXiv: 0907.5520
[16]	Li S H, Shi Q Q, Zhou H Q 2010 arXiv:1001.3343
[17]	Li S H, Shi Q Q, Su Y H, Liu J H, Dai Y W, Zhou H Q 2012 Phys. Rev. B 86 064401
[18]	Li B, Li S H, Zhou H Q 2009 Phys. Rev. E 79 060101(R)
[19]	Li S H, Wang H L, Shi Q Q, Zhou H Q arXiv:1105.3008
[20]	Wang H L, Shi Q Q, Li S H, Zhou H Q arXiv:1106.2129
[21]	Corboz P, White S R, Vidal G, Troyer M 2011 Phys. Rev. B 84 041108(R)
[22]	Murg V, Verstraete F, Cirac J I 2009 Phys. Rev. E 79 195119
[23]	Orús R, Doherty A C, Vidal G 2009 Phys. Rev. Lett. 102 077203
[24]	Bauer B, Vidal G, Troyer M 2009 J. Stat. Mech. 2009 P09006
[25]	Zhou H Q, Orús R, Vidal G 2008 Phys. Rev. Lett. 100 080601
[26]	Suzuki M 1990 Phys. Lett. A 146 319
[27]	Suzuki M 1991 J. Math. Phys. 32 400
[28]	Potts R B 1952 Proc. Cambridge Philos. Soc. 48 106
[29]	Wu F Y 1982 Rev. Mod. Phys. 54 235
[30]	Zhao J H 2012 Acta Phys. Sin. 61 220501 (in Chinese) [赵建辉 2012 61 220501]
[31]	Wang B, Huang H L, Sun Z Y, Kou S P 2012 Chin. Phys. Lett. 29 120301
[32]	Blote H W J, Deng Y 2002 Phys. Rev. E 66 066110
[33]	Crawford J D 1991 Rev. Mod. Phys. 63 991
[34]	Araki J, Yano T, Ueda M, Noda M T 1975 Proc. R. Soc. Lond. A 345 413

施引文献

[1]	Wilson K G 1975 Rev. Mod. Phys. 47 773
[2]	Krishnamurthy H R, Wilkins J W, Wilson K G 1980 Phys. Rev. B 21 1044
[3]	Wilson K G 1971 Phys. Rev. B 4 3174
[4]	Wilson K G 1971 Phys. Rev. B 4 3184
[5]	White S R 1992 Phys. Rev. Lett. 69 2863
[6]	White S R 1992 Phys. Rev. B 48 10345
[7]	Ostlund S, Rommer S 1995 Phys. Rev. Lett. 75 3537
[8]	Verstraete F, Porras D, Cirac J I 2004 Phys. Rev. Lett. 93 227205
[9]	Vidal G 2007 Phys. Rev. Lett. 98 070201
[10]	Murg V, Verstraete F, Cirac J I 2007 Phys. Rev. A 75 033605
[11]	Jordan J, Orús R, Vidal G, Verstraete F, Cirac J I 2008 Phys. Rev. Lett. 101 250602
[12]	Vidal G 2007 Phys. Rev. Lett. 99 220405
[13]	Evenbly G, Vidal G 2009 Phys. Rev. B 79 144108
[14]	Zhao J H, Wang H T 2012 Acta Phys. Sin. 61 220502 (in Chinese) [赵建辉, 王海涛 2012 61 220502]
[15]	Shi Q Q, Li S H, Zhao J H, Zhou H Q 2009 arXiv: 0907.5520
[16]	Li S H, Shi Q Q, Zhou H Q 2010 arXiv:1001.3343
[17]	Li S H, Shi Q Q, Su Y H, Liu J H, Dai Y W, Zhou H Q 2012 Phys. Rev. B 86 064401
[18]	Li B, Li S H, Zhou H Q 2009 Phys. Rev. E 79 060101(R)
[19]	Li S H, Wang H L, Shi Q Q, Zhou H Q arXiv:1105.3008
[20]	Wang H L, Shi Q Q, Li S H, Zhou H Q arXiv:1106.2129
[21]	Corboz P, White S R, Vidal G, Troyer M 2011 Phys. Rev. B 84 041108(R)
[22]	Murg V, Verstraete F, Cirac J I 2009 Phys. Rev. E 79 195119
[23]	Orús R, Doherty A C, Vidal G 2009 Phys. Rev. Lett. 102 077203
[24]	Bauer B, Vidal G, Troyer M 2009 J. Stat. Mech. 2009 P09006
[25]	Zhou H Q, Orús R, Vidal G 2008 Phys. Rev. Lett. 100 080601
[26]	Suzuki M 1990 Phys. Lett. A 146 319
[27]	Suzuki M 1991 J. Math. Phys. 32 400
[28]	Potts R B 1952 Proc. Cambridge Philos. Soc. 48 106
[29]	Wu F Y 1982 Rev. Mod. Phys. 54 235
[30]	Zhao J H 2012 Acta Phys. Sin. 61 220501 (in Chinese) [赵建辉 2012 61 220501]
[31]	Wang B, Huang H L, Sun Z Y, Kou S P 2012 Chin. Phys. Lett. 29 120301
[32]	Blote H W J, Deng Y 2002 Phys. Rev. E 66 066110
[33]	Crawford J D 1991 Rev. Mod. Phys. 63 991
[34]	Araki J, Yano T, Ueda M, Noda M T 1975 Proc. R. Soc. Lond. A 345 413

[1]	李春熠, 莫子夜, 鲁兴业. 铁基超导研究中的单轴应变调控方法. , 2024, 73(19): 197103. doi: 10.7498/aps.73.20241080
[2]	赵秀琴, 张文慧, 王红梅. 非线性相互作用引起的双模Dicke模型的新奇量子相变. , 2024, 73(16): 160302. doi: 10.7498/aps.73.20240665
[3]	陈西浩, 夏继宏, 李孟辉, 翟福强, 朱广宇. 自旋-1/2量子罗盘链的量子相与相变. , 2022, 71(3): 030302. doi: 10.7498/aps.71.20211433
[4]	许霄琰. 强关联电子体系的量子蒙特卡罗计算. , 2022, 71(12): 127101. doi: 10.7498/aps.71.20220079
[5]	保安. 各向异性ruby晶格中费米子体系的Mott相变. , 2021, 70(23): 230305. doi: 10.7498/aps.70.20210963
[6]	尤冰凌, 刘雪莹, 成书杰, 王晨, 高先龙. Jaynes-Cummings晶格模型和Rabi晶格模型的量子相变. , 2021, 70(10): 100201. doi: 10.7498/aps.70.20202066
[7]	陈西浩, 夏继宏, 李孟辉, 翟福强, 朱广宇. 自旋-1/2量子罗盘链的量子相与相变. , 2021, (): . doi: 10.7498/aps.70.20211433
[8]	陈爱民, 刘东昌, 段佳, 王洪雷, 相春环, 苏耀恒. 含有Dzyaloshinskii-Moriya相互作用的自旋1键交替海森伯模型的量子相变和拓扑序标度. , 2020, 69(9): 090302. doi: 10.7498/aps.69.20191773
[9]	文凯, 王良伟, 周方, 陈良超, 王鹏军, 孟增明, 张靖. 超冷⁸⁷Rb原子在二维光晶格中Mott绝缘态的实验实现. , 2020, 69(19): 193201. doi: 10.7498/aps.69.20200513
[10]	黄珊, 刘妮, 梁九卿. 光腔中两组分玻色-爱因斯坦凝聚体的受激辐射特性和量子相变. , 2018, 67(18): 183701. doi: 10.7498/aps.67.20180971
[11]	陈西浩, 王秀娟. 一维扩展量子罗盘模型的拓扑序和量子相变. , 2018, 67(19): 190301. doi: 10.7498/aps.67.20180855
[12]	任杰, 顾利萍, 尤文龙. 带有三体相互作用的S=1自旋链中的保真率和纠缠熵. , 2018, 67(2): 020302. doi: 10.7498/aps.67.20172087
[13]	宋加丽, 钟鸣, 童培庆. 横场中具有周期性各向异性的一维XY模型的量子相变. , 2017, 66(18): 180302. doi: 10.7498/aps.66.180302
[14]	苏耀恒, 陈爱民, 王洪雷, 相春环. 一维自旋1键交替XXZ链中的量子纠缠和临界指数. , 2017, 66(12): 120301. doi: 10.7498/aps.66.120301
[15]	俞立先, 梁奇锋, 汪丽蓉, 朱士群. 双模Dicke模型的一级量子相变. , 2014, 63(13): 134204. doi: 10.7498/aps.63.134204
[16]	赵建辉, 王海涛. 应用多尺度纠缠重整化算法研究量子自旋系统的量子相变和基态纠缠. , 2012, 61(21): 210502. doi: 10.7498/aps.61.210502
[17]	杨金虎, 王杭栋, 杜建华, 张瞩君, 方明虎. Co(S1-xSex)2系统中的铁磁量子相变. , 2009, 58(2): 1195-1199. doi: 10.7498/aps.58.1195
[18]	杨金虎, 王杭栋, 杜建华, 张瞩君, 方明虎. NiS2-xSex在x=1.00附近的反铁磁量子相变. , 2008, 57(4): 2409-2414. doi: 10.7498/aps.57.2409
[19]	蔡卓, 陆文彬, 刘拥军. 交错Dzyaloshinskii-Moriya相互作用对反铁磁Heisenberg链纠缠的影响. , 2008, 57(11): 7267-7273. doi: 10.7498/aps.57.7267
[20]	石筑一, 童红, 石筑亚, 张春梅, 赵行知, 倪绍勇. 转动诱发原子核量子相变的一种可能途径. , 2007, 56(3): 1329-1333. doi: 10.7498/aps.56.1329

计量

文章访问数: 6904
PDF下载量: 635
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板