Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(11): 117501    DOI: 10.1088/1674-1056/20/11/117501
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Translation invariant tensor product states in a finite lattice system

Cai Jian-Wei(蔡建伟)a), Chen Qiao-Ni(陈巧妮)b), Zhao Hui-Hai(赵汇海)a), Xie Zhi-Yuan(谢志远)b), Qin Ming-Pu(秦明普)a) , Wei Zhong-Chao(魏忠超)a), and Xiang Tao(向涛)a)b)†
a Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
Abstract  We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from a same set of local matrices (or tensors) that are determined from an infinite lattice system in one or higher dimensions. This provides an efficient approach for studying translation invariant tensor product states in finite lattice systems. Two methods are introduced to determine the size-independent local tensors.
Keywords:  tensor product state      translation invariant  
Received:  01 April 2011      Revised:  10 August 2011      Accepted manuscript online: 
PACS:  75.10.Jm (Quantized spin models, including quantum spin frustration)  
  75.40.Mg (Numerical simulation studies)  
  05.30.-d (Quantum statistical mechanics)  
  02.70.-c (Computational techniques; simulations)  
Fund: Project supported by the National Natural Science Foundation of China and the National Program for Basic Research of the Ministry of Science and Technology of China.

Cite this article: 

Cai Jian-Wei(蔡建伟), Chen Qiao-Ni(陈巧妮), Zhao Hui-Hai(赵汇海), Xie Zhi-Yuan(谢志远), Qin Ming-Pu(秦明普), Wei Zhong-Chao(魏忠超), and Xiang Tao(向涛) Translation invariant tensor product states in a finite lattice system 2011 Chin. Phys. B 20 117501

[1] White S R 1992 Phys. Rev. Lett. 69 2863
[2] Eisert J, Cramer M and Plenio M B 2010 Rev. Mod. Phys. 82 277 bibitemRommer95 Ostlund S and Rommer S 1995 Phys. Rev. Lett. 75 3537
[3] Verstraete F, Porras D and Cirac J I 2004 Phys. Rev. Lett. 93 227205
[4] Pippan P, White S R and Evertz H G 2010 Phys. Rev. B 81 081103(R)
[5] Pirvu B, Verstraete F and Vidal G 2010 arxiv:1005.5195v1
[6] Sandvik A W and Vidal G 2007 Phys. Rev. Lett. 99 220602
[7] Maeshima N, Hieida Y, Nishino T and Okunishi K 2002 Prog. Theor. Phys. Supplement 145 204
[8] Affleck I, Kennedy T, Lieb E H and Tasaki H 1998 Commun. Math. Phys. 115 477
[9] McCulloch I 2008 arXiv:0804.2509
[10] Ueda H, Gendiar A and Nishino T 1999 J. Phys. Soc. Jpn. 79 044001
[11] Rommer S and Ostlund S 1997 Phys. Rev. B 55 2164
[12] Jiang H C, Weng Z Y and Xiang T 2008 Phys. Rev. Lett. 101 090603
[13] Zhao H H, Xie Z Y, Chen Q N, Wei Z C, Cai J W and Xiang T 2010 Phys. Rev. B 81 174411
[14] Perez-Garcia D, Verstraete F, Wolf M M and Cirac J I 2007 Quantum Inf. Comput. 7 401
[15] Vidal G 2007 Phys. Rev. Lett. 98 070201
[16] Xie Z Y, Jiang H C, Chen Q N, Weng Z Y and Xiang T 2009 Phys. Rev. Lett. 103 160601
[17] Orus R and Vidal G 2008 Phys. Rev. B 78 155117
[18] Mederiros D and Cabrera G G 1991 Phys. Rev. B 43 3703
[1] Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J1-J2 Heisenberg model
He-Yu Lin(林赫羽), Rong-Qiang He(贺荣强), and Zhong-Yi Lu(卢仲毅). Chin. Phys. B, 2022, 31(8): 080203.
[2] Gauss quadrature based finite temperature Lanczos method
Jian Li(李健) and Hai-Qing Lin(林海青). Chin. Phys. B, 2022, 31(5): 050203.
[3] Structure and frustrated magnetism of the two-dimensional triangular lattice antiferromagnet Na2BaNi(PO4)2
Fei Ding(丁飞), Yongxiang Ma(马雍翔), Xiangnan Gong(公祥南), Die Hu(胡蝶), Jun Zhao(赵俊), Lingli Li(李玲丽), Hui Zheng(郑慧), Yao Zhang(张耀), Yongjiang Yu(于永江), Lichun Zhang(张立春), Fengzhou Zhao(赵风周), and Bingying Pan(泮丙营). Chin. Phys. B, 2021, 30(11): 117505.
[4] LnCu3(OH)6Cl3 (Ln = Gd, Tb, Dy): Heavy lanthanides on spin-1/2 kagome magnets
Ying Fu(付盈), Lianglong Huang(黄良龙), Xuefeng Zhou(周雪峰), Jian Chen(陈见), Xinyuan Zhang(张馨元), Pengyun Chen(陈鹏允), Shanmin Wang(王善民), Cai Liu(刘才), Dapeng Yu(俞大鹏), Hai-Feng Li(李海峰), Le Wang(王乐), and Jia-Wei Mei(梅佳伟). Chin. Phys. B, 2021, 30(10): 100601.
[5] Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder
Cong Fu(傅聪), Hui Zhao(赵晖), Yu-Guang Chen(陈宇光), and Yong-Hong Yan(鄢永红). Chin. Phys. B, 2021, 30(8): 087501.
[6] Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets
Guangyu Sun(孙光宇), Nvsen Ma(马女森), Bowen Zhao(赵博文), Anders W. Sandvik, and Zi Yang Meng(孟子杨). Chin. Phys. B, 2021, 30(6): 067505.
[7] Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions
Fa-Kai Wen(温发楷) and Xin Zhang(张鑫). Chin. Phys. B, 2021, 30(5): 050201.
[8] Origin of itinerant ferromagnetism in two-dimensional Fe3GeTe2
Xi Chen(陈熙), Zheng-Zhe Lin(林正喆), and Li-Rong Cheng(程丽蓉). Chin. Phys. B, 2021, 30(4): 047502.
[9] Some experimental schemes to identify quantum spin liquids
Yonghao Gao(高永豪), Gang Chen(陈钢). Chin. Phys. B, 2020, 29(9): 097501.
[10] Tunable deconfined quantum criticality and interplay of different valence-bond solid phases
Bowen Zhao(赵博文), Jun Takahashi, Anders W. Sandvik. Chin. Phys. B, 2020, 29(5): 057506.
[11] High pressure synthesis and characterization of the pyrochlore Dy2Pt2O7: A new spin ice material
Qi Cui(崔琦), Yun-Qi Cai(蔡云麒), Xiang Li(李翔), Zhi-Ling Dun(顿志凌), Pei-Jie Sun(孙培杰), Jian-Shi Zhou(周建十), Hai-Dong Zhou(周海东), Jin-Guang Cheng(程金光). Chin. Phys. B, 2020, 29(4): 047502.
[12] Quantum coherence and correlation dynamics of two-qubit system in spin bath environment
Hao Yang(杨豪), Li-Guo Qin(秦立国), Li-Jun Tian(田立君), Hong-Yang Ma(马鸿洋). Chin. Phys. B, 2020, 29(4): 040303.
[13] Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling
Jiayu Xie(谢家玉), Zhihao Deng(邓志豪), Xia Chang(昌霞), Bing Tang(唐炳). Chin. Phys. B, 2019, 28(7): 077501.
[14] Quantum steering in Heisenberg models with Dzyaloshinskii-Moriya interactions
Hui-Zhen Li(李慧贞), Rong-Sheng Han(韩榕生), Ye-Qi Zhang(张业奇), Liang Chen(陈亮). Chin. Phys. B, 2018, 27(12): 120304.
[15] Modulational instability, quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field
Wanhan Su(苏琬涵), Jiayu Xie(谢家玉), Tianle Wu(吴天乐), Bing Tang(唐炳). Chin. Phys. B, 2018, 27(9): 097501.
No Suggested Reading articles found!