Abstract.
The Landau-Zener (LZ) transition of a two-level system coupling to spin chains near their critical points is studied in this paper. Two kinds of spin chains, the Ising spin chain and XY spin chain, are considered. We calculate and analyze the effects of system-chain coupling on the LZ transition. A relation between the LZ transition and the critical points of the spin chain is established. These results suggest that LZ transitions may serve as the witnesses of criticality of the spin chain. This may provide a new way to study quantum phase transitions as well as LZ transitions.
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References
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambrage, New York, 2000)
A. Izmalkov et al., Europhys. Lett. 65, 844 (2004)
W.D. Oliver, Y. Yu, J.C. Lee, K.K. Berggren, L.S. Levitov, T.P. Orlando, Science 310, 1653 (2005)
M. Sillanpää, T. Lehtinen, A. Paila, Y. Makhlin, P. Hakonen, Phys. Rev. Lett. 96, 187002 (2006)
L.D. Landau, Phys. Z. Sowj. 2, 46 (1932)
C. Zener, Proc. R. Soc. A 137, 696 (1932)
E.C.G. Stueckelberg, Helv. Phys. Acta 5, 369 (1932)
E. Majorana, Nuovo Cim. 9, 43 (1932)
J. Ankerhold, H. Grabert, Phys. Rev. Lett. 91, 016803 (2003)
K. Saito, Y. Kayanuma, Phys. Rev. B 70, 201304(R) (2004)
K. Saito, M. Wubs, S. Kohler, P. Hänggi, Y. Kayanuma, Europhys. Lett. 76, 22 (2006)
M. Wubs, S. Kohler, P. Hänggi, e-print arXiv:cond-mat/0703425
C. Hicke, L.F. Santos, M.I. Dykman, Phys. Rev. A 73, 012342 (2006)
Y. Kayanuma, Phys. Rev. Lett. 58, 1934 (1987); P. Ao, J. Rammer, Phys. Rev. Lett. 62, 3004 (1989); E. Shimshoni, A. Stern, Phys. Rev. B 47, 9523 (1992)
M. Wubs, K. Saito, S. Kohler, P. Hänggi, Y. Kayanuma, Phys. Rev. Lett. 97, 200404 (2006)
K. Saito, M. Wubs, S. Kohler, Y. Kayanuma, P. Hänggi, e-print arXiv:cond-mat/0703596
M. Wubs, K. Saito, S. Kohler, Y. Kayanuma, P. Hänggi, New J. Phys. 7, 218 (2005)
A.T.S. Wan, M.H.S. Amin, S. Wang, e-print arXiv:cond-mat/0703085
S. Sachdev, Quantum Phase Transition (Cambridge University Press, Cambridge, 1999)
T.J. Osborne, M.A. Nielsen, Phys. Rev. A 66, 032110 (2002); L.-A. Wu, M.S. Sarandy, D.A. Lidar, Phys. Rev. Lett. 93, 250404 (2004); S.J. Gu, S.S. Deng, Y.Q. Li, H.Q. Lin, Phys. Rev. Lett. 93, 086402 (2004)
A.C.M. Carollo, K. JPachos, Phys. Rev. Lett. 95, 157203 (2005); S.L. Zhu, Phys. Rev. Lett. 96, 077206 (2006)
P. Zanardi, M. Cozzini, P. Giorda, e-print quant-ph/0606130; P. Zanardi, H.T. Quan, X. Wang, C.P. Sun, Phys. Rev. A 75, 032109 (2007)
H.T. Quan, Z. Song, X.F. Liu, P. Zanardi, C.P. Sun, Phys. Rev. Lett. 96, 140604 (2006)
X.X. Yi, H.T. Cui, L.C. Wang, Phys. Rev. A 74, 054102 (2006)
Z.G. Yuan, P. Zhang, S.S. Li, Phys. Rev. A 75, 012102 (2007)
X.X. Yi, W. Wang, Phys. Rev. A 75, 032103 (2007)
W.H. Zurek, U. Dorner, P. Zoller, Phys. Rev. Lett. 95, 105701 (2005)
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Wang, L., Huang, X. & Yi, X. Landau-Zener transition of a two-level system driven by spin chains near their critical points. Eur. Phys. J. D 46, 345–349 (2008). https://doi.org/10.1140/epjd/e2007-00286-2
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DOI: https://doi.org/10.1140/epjd/e2007-00286-2