Simulation of two-dimensional quantum systems on an infinite lattice revisited: Corner transfer matrix for tensor contraction

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 9, 2009, Pages

  Orús, Román ^a   Vidal, Guifré ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70349976288     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.094403     Document Type: Article

References (28)

1. F. Verstraete and J. Cirac, arXiv:cond-mat/0407066 (unpublished);
2. V. Murg, F. Verstraete, and J. I. Cirac, Phys. Rev. A 75, 033605 (2007). 10.1103/PhysRevA.75.033605
3. J. Jordan, R. Orús, G. Vidal, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 101, 250602 (2008). 10.1103/PhysRevLett.101.250602
4. G. Sierra and M. Martín-Delgado, arXiv:cond-mat/9811170 (unpublished).
5. T. Nishino and K. Okunishi, J. Phys. Soc. Jpn. 67, 3066 (1998). 10.1143/JPSJ.67.3066
6. Y. Nishio, N. Maeshima, A. Gendiar, and T. Nishino, arXiv:cond-mat/ 0401115 (unpublished).
7. Z.-Cheng Gu, M. Levin, and X.-Gang Wen, Phys. Rev. B 78, 205116 (2008). 10.1103/PhysRevB.78.205116
8. H. C. Jiang, Z. Y. Weng, and T. Xiang, Phys. Rev. Lett. 101, 090603 (2008). 10.1103/PhysRevLett.101.090603
9. A. Isacsson and O. F. Syljuasen, Phys. Rev. E 74, 026701 (2006) 10.1103/PhysRevE.74.026701
10. H-Q. Zhou, R. Orús, and G. Vidal, Phys. Rev. Lett. 100, 080601 (2008). 10.1103/PhysRevLett.100.080601
11. R. Orús, A. C. Doherty, and G. Vidal, Phys. Rev. Lett. 102, 077203 (2009). 10.1103/PhysRevLett.102.077203
12. B. Li, S. Li, and H. Zhou, Phys. Rev. E 79, 060101 (R) (2009). 10.1103/PhysRevE.79.060101
13. J. Jordan, R. Orús, and G. Vidal, Phys. Rev. B 79, 174515 (2009). 10.1103/PhysRevB.79.174515
14. V. Murg, F. Verstraete, and J. Cirac, Phys. Rev. B 79, 195119 (2009). 10.1103/PhysRevB.79.195119
15. B. Bauer, G. Vidal, and M. Troyer, arXiv:0905.4880 (unpublished).
16. G. Vidal, Phys. Rev. Lett. 98, 070201 (2007) 10.1103/PhysRevLett.98. 070201
17. R. Orús and G. Vidal, Phys. Rev. B 78, 155117 (2008). 10.1103/PhysRevB.78.155117
18. T. Nishino and K. Okunishi, J. Phys. Soc. Jpn. 65, 891 (1996). 10.1143/JPSJ.65.891
19. R. J. Baxter, J. Math. Phys. 9, 650 (1968) 10.1063/1.1664623
20. R. J. Baxter, J. Stat. Phys. 19, 461 (1978) 10.1007/BF01011693
21. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
22. The accuracies obtained in this work for the critical point of the 2D quantum Ising model are comparable to those obtained in Ref. for the 3D classical Ising model. The present approach, also valid for 2D quantum systems without 3D classical counterpart, does not suffer from the instabilities reported in Ref.
23. T. Nishino, Y. Hieida, K. Okunishi, N. Maeshima, and Y. Akutsu, Prog. Theor. Phys. 105, 409 (2001) 10.1143/PTP.105.409
24. A. Gendiar, N. Maeshima, and T. Nishino, Prog. Theor. Phys. 110, 691 (2003) 10.1143/PTP.110.691
25. A. Gendiar, T. Nishino, and R. Derian, Acta Phys. Slov. 55, 141 (2005).
26. M. Levin and C. P. Nave, Phys. Rev. Lett. 99, 120601 (2007). 10.1103/PhysRevLett.99.120601
27. H. W. J. Blöte and Y. Deng, Phys. Rev. E 66, 066110 (2002). 10.1103/PhysRevE.66.066110
28. L. Tagliacozzo, T. R. de Oliveira, S. Iblisdir, and J. I. Latorre, Phys. Rev. B 78, 024410 (2008). 10.1103/PhysRevB.78.024410