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Global Entanglement Measures and Quantum Phase Transitions in the 1D J 1−J 2 Model

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Abstract

We have analyzed the behavior of multipartite global entanglement and average bipartite concurrence for the sign of quantum phase transitions in the frustrated J 1−J 2 model by using exact diagonalization technique for a chain of 12 qubits. It is found that although the magnitude of two classes of the measures show opposite trends the absolute value of their derivatives show similar structure near critical points.

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References

  1. Amico, L., Fazio, R., Osterloh, R., Vedral, V.: Preprint, arXiv:quant-ph/0703044 (2007)

  2. Osterloh, R., Amico, L., Falci, G., Fazio, R.: Nature (London) 416, 608 (2002)

    Article  ADS  Google Scholar 

  3. Osborne, T.J., Nielsen, M.A.: Phys. Rev. A 66, 032110 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  4. Glase, U., Büttner, H., Freske, H.: Phys. Rev. A 68, 032318 (2003)

    Article  ADS  Google Scholar 

  5. Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Phys. Rev. Lett. 90, 227902 (2003)

    Article  ADS  Google Scholar 

  6. Verstraete, F., Popp, M., Cirac, J.I.: Phys. Rev. Lett. 92, 027901 (2004)

    Article  ADS  Google Scholar 

  7. Gu, S., Deng, S., Li, Y., Ling, H.: Phys. Rev. Lett. 93, 086402 (2004)

    Article  ADS  Google Scholar 

  8. Latorre, J.I., Rico, E., Vidal, G.: Quantum Inf. Comput. 4, 48 (2004)

    MATH  MathSciNet  Google Scholar 

  9. Somma, R., Ortiz, G., Barnum, H., Knill, E., Viola, L.: Phys. Rev. A 70, 042311 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  10. Yang, M.F.: Phys. Rev. A 71, 030302(R) (2005)

    ADS  Google Scholar 

  11. Wei, T.-C., Goldbart, P.M.: Phys. Rev. A 68, 042307 (2003)

    Article  ADS  Google Scholar 

  12. Wei, T.-C., Das, D., Mukhopadyay, S., Wisheshwera, S., Goldbart, P.: Phys. Rev. A 71, 060305 (2005)

    Article  ADS  Google Scholar 

  13. Meyer, D.A., Wallach, N.R.: J. Math. Phys. 43, 4273 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. de Oliveira, T.R., Rigolin, G., de Oliveira, M.C.: Phys. Rev. A 73, 010305(R) (2006)

    Google Scholar 

  15. Rigolin, G., de Oliveira, T.R., de Oliveira, M.C.: Phys. Rev. A 74, 022314 (2006). See also the erratum: G. Rigolin, T.R. de Oliveira and M.C. de Oliveira Phys. Rev. A 75, 049904(E) (2007)

    Article  ADS  Google Scholar 

  16. de Oliveira, T.R., Rigolin, G., de Oliveira, M.C., Miranda, E.: Phys. Rev. Lett. 97, 170401 (2006)

    Article  Google Scholar 

  17. Roscilde, T., Verrucchi, P., Fubini, A., Haas, S., Tognetti, V.: Preprint, arXiv:quant-ph/0412056 (2004)

  18. Roscilde, T., Verrucchi, P., Fubini, A., Haas, S., Tognetti, V.: Phys. Rev. Lett. 94, 147208 (2005)

    Article  ADS  Google Scholar 

  19. Nomura, K., Okamoto, K.: J. Phys. A 27, 5773 (1994)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  20. Hirata, S., Nomura, K.: Phys. Rev. B 61, 9453 (2000)

    Article  ADS  Google Scholar 

  21. Gerhardt, C., Mütter, K.-H., Kröger, H.: Phys. Rev. B 57, 11504 (1998)

    Article  Google Scholar 

  22. Verkholyak, T., Honecker, A., Brenig, W.: Preprint, arXiv:cond-mat/0505654 (2005)

  23. Lu, H.T., Wang, Y.J., Qin, S., Xiang, T.: Phys. Rev. B 74, 134425 (2006)

    Article  ADS  Google Scholar 

  24. Eryiğit, R., Eryiğit, R., Gündüç, Y.: Int. J. Mod. Phys. C 15, 1095 (2004)

    Article  MATH  ADS  Google Scholar 

  25. Qian, X.-F., Shi, T., Li, Y., Song, Z., Sun, C.-P.: Phys. Rev. A 72, 012333 (2005)

    Article  ADS  Google Scholar 

  26. Eryiğit, R., Gündüç, Y., Eryiğit, R.: Phys. Lett. A 349, 37 (2006)

    Article  ADS  Google Scholar 

  27. Chhajlany, R.W., Tomczak, P., Wojcik, A., Richter, J.: Preprint, arXiv:cond-mat/0610379 (2006)

  28. Wootters, W.K.: Phys. Rev. Lett. 80, 2245 (1998)

    Article  Google Scholar 

  29. Vidal, G., Werner, R.F.: Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  30. Brennen, G.K.: Quantum Inf. Comput. 3, 619 (2003)

    MATH  MathSciNet  Google Scholar 

  31. Lakshminarayan, A., Subrahmanyam, V.: Phys. Rev. A 71, 062334 (2005)

    Article  ADS  Google Scholar 

  32. Barnum, H., Knill, E., Ortiz, G., Somma, R., Viola, L.: Phys. Rev. Lett. 92, 107902 (2004)

    Article  ADS  Google Scholar 

  33. Majumdar, C.K., Ghosh, D.K.: J. Math. Phys. 10, 1388 (1969)

    Article  ADS  MathSciNet  Google Scholar 

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  1. Department of Computer Engineering, Pamukkale University, Denizli, 20100, Turkey

    Recep Eryiğit

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  1. Recep Eryiğit
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Eryiğit, R. Global Entanglement Measures and Quantum Phase Transitions in the 1D J 1−J 2 Model. Int J Theor Phys 48, 885–893 (2009). https://doi.org/10.1007/s10773-008-9861-4

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  • DOI: https://doi.org/10.1007/s10773-008-9861-4

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