Quantum fidelity and quantum phase transitions in matrix product states

Physical Review B - Condensed Matter and Materials Physics

Volumn 76, Issue 10, 2007, Pages

  Cozzini, Marco ^a,b   Ionicioiu, Radu ^b,d   Zanardi, Paolo ^b,c  

^a POLITECNICO DI TORINO   (Italy)

^b ISI FOUNDATION   (Italy)

^c UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^d HEWLETT PACKARD LABORATORIES   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34648814053     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.76.104420     Document Type: Article

References (22)

1. P. Zanardi and N. Paunković, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.031123 74, 031123 (2006);
2. P. Zanardi, M. Cozzini, and P. Giorda, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 (2007) L02002.
3. M. Cozzini, P. Giorda, and P. Zanardi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.014439 75, 014439 (2007).
4. H.-Q. Zhou and J. P. Barjaktarevič, arXiv:cond-mat/0701608 (unpublished).
5. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.799 59, 799 (1987);
6. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01218021 115, 477 (1988).
7. M. Fannes, B. Nachtergaele, and R. F. Werner, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/10/7/005 10, 633 (1989);
8. M. Fannes, B. Nachtergaele, and R. F. Werner, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF02099178 144, 443 (1992);
9. S. Östlund and S. Rommer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.3537 75, 3537 (1995);
10. S. Rommer and S. Östlund, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.55.2164 55, 2164 (1997).
11. D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, Quantum Inf. Comput. QICUAW 1533-7146 7, 401 (2007).
12. 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).
13. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902 90, 227902 (2003);
14. G. Refael and J. E. Moore, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.260602 93, 260602 (2004);
15. V. E. Korepin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 096402 92, 096402 (2004).
16. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002).
17. G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.147902 91, 147902 (2003).
18. M. E. Fisher and M. N. Barber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.28.1516 28, 1516 (1972);
19. M. N. Barber, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, J. L. Lebowitz, (Academic, London, 1983), Vol. 8, p. 145.
20. R. H. Dicke, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.93.99 93, 99 (1954).
21. W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 2245 80, 2245 (1998).
22. By using Uhlmann's fidelity for mixed states, one can extend this kind of analysis to finite temperature systems and therefore even to classical phase transitions. See Ref. and P. Zanardi, H.-T. Quan, X.-G. Wang, and C.-P. Sun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.032109 75, 032109 (2007).