Matrix product states: Symmetries and two-body Hamiltonians

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 79, Issue 4, 2009, Pages

  Sanz, M ^a   Wolf, M M ^b   Perez Garcia D ^c   Cirac, J I ^a  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BASIC RESULTS; EXHAUSTIVE SEARCHES; LOCAL TRANSFORMATIONS; MANY BODIES; MATRIX-PRODUCT STATE; SYMMETRY GROUPS;

HAMILTONIANS; QUANTUM THEORY;

MAGNETOPLASMA;

EID: 64649102065     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.79.042308     Document Type: Article

References (23)

1. M. Fannes, B. Nachtergaele, and R. W. Werner, Commun. Math. Phys. 144, 443 (1992). 10.1007/BF02099178
2. D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, Quantum. Inf. Comput. 7, 401 (2007).
3. D. Perez-Garcia, M. M. Wolf, M. Sanz, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 100, 167202 (2008). 10.1103/PhysRevLett.100.167202
4. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. 115, 477 (1988). 10.1007/BF01218021
5. C. K. Majumdar and D. K. Ghosh, J. Math. Phys. 10, 1399 (1969). 10.1063/1.1664979
6. F. D. M. Haldane, Phys. Lett. A 93, 464 (1983) 10.1016/0375-9601(83) 90631-X
7. F. D. M. Haldane, Phys. Rev. Lett. 50, 1153 (1983). 10.1103/PhysRevLett. 50.1153
8. A. Klümper, A. Schadschneider, and J. Zittartz, Europhys. Lett. 24, 293 (1993). 10.1209/0295-5075/24/4/010
9. V. Karimipour and L. Memarzadeh, Phys. Rev. B 77, 094416 (2008). 10.1103/PhysRevB.77.094416
10. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. 16, 407 (1961). 10.1016/0003-4916(61)90115-4
11. M. B. Hastings, Phys. Rev. B 69, 104431 (2004). 10.1103/PhysRevB.69. 104431
12. F. Verstraete and J. I. Cirac, Phys. Rev. B 73, 094423 (2006). 10.1103/PhysRevB.73.094423
13. Eventually after gathering some spins together to neglect the periodic components-something that we will always assume.
14. The condition of Ref. (theorem 311) that the canonical form in the OBC must be unique can be dropped by Eq. 3 of L. Lamata, Phys. Rev. Lett. 101, 180506 (2008). 10.1103/PhysRevLett.101.180506
15. S. Singh, H.-Q. Zhou, and G. Vidal, e-print arXiv:cond-mat/0701427.
16. J. Dukelsky, M. A. Martin-Delgado, T. Nishino, and G. Sierra, Europhys. Lett. 43, 457 (1998). 10.1209/epl/i1998-00381-x
17. B. Kumar, Phys. Rev. B 66, 024406 (2002). 10.1103/PhysRevB.66.024406
18. J. M. Roman, G. Sierra, J. Dukelsky, and M. A. Martin-Delgado, J. Phys. A 31, 9729 (1998). 10.1088/0305-4470/31/48/009
19. S. Rachel and M. Greiter, Phys. Rev. B 78, 134415 (2008). 10.1103/PhysRevB.78.134415
20. D. Sen and N. Surendran, Phys. Rev. B 75, 104411 (2007). 10.1103/PhysRevB.75.104411
21. The family of Hamiltonians constructed in is quite remarkable. In this paper the ground state of the Hamiltonian which corresponds to b=2a is calculated and fits perfectly to our results.
22. O. Bratteli, P. E. T. Jorgensen, A. Kishimoto, and R. F. Werner, J. Oper. Theory 43, 97 (2000).
23. Hong-Hao Tu, Guang-Ming Zhang, and Tao Xiang, Phys. Rev. B 78, 094404 (2008). 10.1103/PhysRevB.78.094404