Lieb-Robinson bounds on the speed of information propagation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 81, Issue 6, 2010, Pages

  Prémont Schwarz, Isabeau ^a,b   Hnybida, Jeff ^a,b  

^a PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDED OPERATORS; FINITE NUMBER; GENERAL GRAPH; INFORMATION PROPAGATION; INTERACTION STRENGTH; PROPAGATION SPEED; QUANTUM PHASE TRANSITIONS; QUANTUM SYSTEM; ROBINSON; SPEED OF PROPAGATION; UNBOUNDED OPERATORS;

HAMILTONIANS; QUANTUM ELECTRONICS; QUANTUM OPTICS; SPEED;

PHASE TRANSITIONS;

EID: 77953598966     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.062107     Document Type: Article

References (26)

1. E. H. Lieb and D. W. Robinson, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01645779 28, 251 (1972).
2. M. B. Hastings, Phys. Rev. B CMPHAY 1098-0121 10.1103/PhysRevB.69.104431 69, 104431 (2004).
3. B. Nachtergaele and R. Sims, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-006-1556-1 265, 119 (2006).
4. B. Nachtergaele, Y. Ogata, and R. Sims, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-006-9143-6 124, 1 (2006).
5. S. Bravyi, M. B. Hastings, and F. Verstraete, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.050401 97, 050401 (2006).
6. M. Cramer and J. Eisert, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/5/071 8, 71 (2006).
7. J. Eisert and T. J. Osborne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.150404 97, 150404 (2006).
8. N. Schuch, J. I. Cirac, M. M. Wolf, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-006-0049-6 267, 65 (2006).
9. M. B. Hastings and T. Koma, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-006-0030-4 265, 781 (2006).
10. J. Eisert, M. B. Plenio, S. Bose, and J. Hartley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.190402 93, 190402 (2004).
11. M. B. Plenio, J. Hartley, and J. Eisert, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/6/1/036 6, 36 (2004).
12. P. Coleman and A. J. Schofield, Nature (London) NATUAS 0028-0836 10.1038/nature03279 433, 226 (2005).
13. J. A. Hertz, Phys. Rev. B NATUAS 1098-0121 10.1103/PhysRevB.14.1165 14, 1165 (1976).
14. J. B. Kogut, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.51.659 51, 659 (1979).
15. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, UK, 1999).
16. R. B. Laughlin, G. G. Lonzarich, P. Monthoux, and D. Pines, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730110098534 50, 361 (2001).
17. A. Hamma, F. Markopoulou, I. Prémont-Schwarz, and S. Severini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.017204 102, 017204 (2009).
18. I. Prémont-Schwarz, A. Hamma, I. Klich, and F. Markopoulou, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.040102 81, 040102 (R) (2010).
19. T. Konopka, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.78.044032 78, 044032 (2008).
20. T. Konopka, F. Markopoulou, and S. Severini, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.77.104029 77, 104029 (2008).
21. J. Eisert and D. Gross, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.240501 102, 240501 (2009).
22. M. Cramer, A. Serafini, and J. Eisert, in Quantum Information and Many Body Quantum Systems, edited by, M. Eriksson, and, S. Montangero, (Edizioni della Normale, Pisa, 2008).
23. R. B. Stinchcombe, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/6/15/009 6, 2459 (1973).
24. G. P. Berman, G. D. Doolen, D. D. Holm, and V. I. Tsifrinovich, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(94)90537-1 193, 444 (1994).
25. T. Schneider and J. M. Singer, Physica C PHYCE6 0921-4534 10.1016/S0921-4534(00)00397-X 341-348, 87 (2000).
26. A. S. T. Pires, L. S. Lima, and M. E. Gouvea, J. Phys. JCOMEL 0953-8984 10.1088/0953-8984/20/01/015208 20, 015208 (2008).