Entangled rings, matrix product states, and exact solutions of XYZ spin chains

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 76, Issue 1, 2007, Pages

  Asoudeh, Marzieh ^a   Karimipour, Vahid ^a   Sadrolashrafi, Afsaneh ^a  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF STATE; MAGNETIC FIELD EFFECTS; QUANTUM THEORY; SURFACE PROPERTIES; TWO DIMENSIONAL;

COUPLING CONSTANTS; ENTANGLED RINGS; MATRIX PRODUCT STATES; SPIN CHAINS;

GROUND STATE;

EID: 34547149561     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.012320     Document Type: Article

References (22)

1. K. M. O'Connor and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.052302 63, 052302 (2001).
2. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature NATUAS 0028-0836 10.1038/416608a 416, 608 (2002)
3. T. J. Osborne and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032110 66, 032110 (2002)
4. M. C. Arnesen S. Bose, and V. Vedral, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.017901 87, 017901 (2001)
5. M. Asoudeh and V. Karimipour, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.052307 70, 052307 (2004)
6. A. R. Its, B.-Q. Jin, and V. E. Korepin, J. Phys. A JPHAC5 0305-4470 38, 2975 (2005).
7. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.799 59, 799 (1987).
8. M. Fannes, B. Nachtergaele, and R. F. Werner, Europhys. Lett. EULEEJ 0295-5075 10 633 (1989)
9. A. Klumper, A. Schadschneider, and J. Zittartz, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/24/16/012 24 L955 (1991)
10. A. Klumper, A. Schadschneider, and J. Zittartz, J. Phys. A JPHAC5 0305-4470 87, 281 (1992).
11. F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.087201 92, 087201 (2004)
12. F. Verstraete, M. Popp, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.027901 92, 027901 (2004)
13. F. Verstraete, J. I. Cirac, J. I. Latorre, E. Rico, and M. M. Wolf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.140601 94, 140601 (2005).
14. M. M. Wolf, G. Ortiz, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.110403 97, 110403 (2006).
15. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999).
16. C. K. Majumdar, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/3/4/019 3, 911 (1970).
17. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. ANPYA2 0003-3804 10.1016/0003-4916(61)90115-4 16, 407 (1961).
18. W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 2245 80, 2245 (1998).
19. With conditions 12, the matrix ρ ρ has only two nonzero eigenvalues given by λ1,2 = 1 4 (Gy ± Gz) 2, which gives C= |λ1 - λ2|.
20. For η=-1 and N=odd such an MPS does not exist, i.e., Ψ is identical to zero. One can prove this by induction using the facts that tr (A0) =tr (A1) =0, and A02, A12, and A0 A1 + A1 A0 are all proportional to identity.
21. J. Kurmann, H. Thomas, and G. Müller, Physica A PHYADX 0378-4371 10.1016/0378-4371(82)90217-5 112, 235 (1982)
22. G. Müller and R. E. Shrock, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.32.5845 32, 5845 (1985).