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Brazilian Journal of Physics

, Volume 46, Issue 3, pp 239–247 | Cite as

Survival Probability of the Néel State in Clean and Disordered Systems: An Overview

  • E. J. Torres-Herrera
  • Marco Távora
  • Lea F. SantosEmail author
Condensed Matter

Abstract

In this work we provide an overview of our recent results about the quench dynamics of one-dimensional many-body quantum systems described by spin-1/2 models. To illustrate those general results, here we employ a particular and experimentally accessible initial state, namely the Néel state. Both cases are considered: clean chains without any disorder and disordered systems with static random on-site magnetic fields. The quantity used for the analysis is the probability for finding the initial state later in time, the so-called survival probability. At short times, the survival probability may decay faster than exponentially, Gaussian behaviors and even the limit established by the energy-time uncertainty relation are displayed. The dynamics at long times slows down significantly and shows a powerlaw behavior. For both scenarios, we provide analytical expressions that agree very well with our numerical results.

Keywords

Non-equilibrium quantum physics Quench dynamics Spin systems Disordered systems 

Notes

Acknowledgments

This work was motivated by a presentation given by one of the authors at the Workshop: Quantum Information and Thermodynamics held in São Carlos in February, 2015. This work was supported by the NSF grant No. DMR-1147430. E.J.T.H. acknowledges support from CONACyT, Mexico. LFS thanks the ITAMP hospitality, where part of this work was done.

References

  1. 1.
    E.J. Torres-Herrera, L.F. Santos, Phys. Rev. B 92, 014208 (2015)ADSCrossRefGoogle Scholar
  2. 2.
    E.J. Torres-Herrera, L.F. Santos, Phys. Rev. A 043620, 89 (2014)Google Scholar
  3. 3.
    E.J. Torres-Herrera, M. Vyas, L.F. Santos, J. New, Phys. 063010, 16 (2014)Google Scholar
  4. 4.
    E.J. Torres-Herrera, L.F. Santos, Phys. Rev. A 033623, 90 (2014)Google Scholar
  5. 5.
    E.J. Torres-Herrera, L.F. Santos, Phys. Rev. E 062110, 89 (2014)Google Scholar
  6. 6.
    E.J. Torres-Herrera, L.F. Santos, ed. by P. Danielewicz, V. Zelevinsky. in AIP Proceedings, (APS, East Lansing Michigan , 2014)Google Scholar
  7. 7.
    E.J. Torres-Herrera, D. Kollmar, L.F. Santos, Relaxation and thermalization of isolated many-body quantum systems. arXiv:1403.6481 (2015)
  8. 8.
    E.J. Torres-Herrera, L.F. Santos, Phys. Rev. E 042121, 88 (2013)Google Scholar
  9. 9.
    T.B. Batalhão, A.M. Souza, L. Mazzola, R. Auccaise, R.S. Sarthour, I.S. Oliveira, J. Goold, G. De Chiara, M. Paternostro, R.M. Serra, Phys. Rev. Lett. 140601, 113 (2014)Google Scholar
  10. 10.
    P. Cappellaro, C. Ramanathan, D.G. Cory, Phys. Rev. Lett. 250506, 99 (2007)Google Scholar
  11. 11.
    G. Kaur, A. Ajoy, P. Cappellaro, J. New, Phys. 15, 093035 (2013)Google Scholar
  12. 12.
    P. Jurcevic, B.P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, C.F. Roos, Nature. 511, 202 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    P. Richerme, Z.X. Gong, A. Lee, C. Senko, J. Smith, M. Foss-Feig, S. Michalakis, A.V. Gorshkov, C. Monroe, Nature. 511(7508), 198 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A.M. Rey, A. Polkovnikov, E.A. Demler, M.D. Lukin, I. Bloch, Science. 319, 295 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    S. Trotzky, Y.A. Chen, A. Flesch, I.P. McCulloch, U. Schollwöck, J. Eisert, I. Bloch, Nat. Phys. 8, 325 (2012)CrossRefGoogle Scholar
  16. 16.
    T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schausz, S. Hild, D. Bellem, U. Schollwöck, T. Giamarchi, C. Gross, I. Bloch, S. Kuhr, Nat. Phys. 9, 235 (2013)CrossRefGoogle Scholar
  17. 17.
    L.A. Khalfin, Sov. Phys. JETP. 6, 1053 (1958)ADSGoogle Scholar
  18. 18.
    L. Fonda, G.C. Ghirardi, A. Rimini, Rep. Prog. Phys. 41, 587 (1978)ADSCrossRefGoogle Scholar
  19. 19.
    A. del Campo, Phys. Rev. A. 012113, 84 (2011)Google Scholar
  20. 20.
    A. del Campo, arXiv:1504.01620
  21. 21.
    J.G. Muga, A. Ruschhaupt, A. del Campo. Time in Quantum Mechanics, vol. 2. (Springer, London, 2009)CrossRefzbMATHGoogle Scholar
  22. 22.
    C. Rothe, S.I. Hintschich, A.P. Monkman, Phys. Rev. Lett. 163601, 96 (2006)Google Scholar
  23. 23.
    F.M. Izrailev, A. Castaṅeda-Mendoza, Phys. Lett. A 350, 355 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    H.A. Bethe, Z. Phys. 71, 205 (1931)ADSCrossRefGoogle Scholar
  25. 25.
    Y. Avishai, J. Richert, R. Berkovitz, Phys. Rev. B 66(052416), 1 (2002)Google Scholar
  26. 26.
    L.F. Santos, G. Rigolin, C.O. Escobar, Phys. Rev. A 042304, 69 (2004)MathSciNetGoogle Scholar
  27. 27.
    F. Dukesz, M. Zilbergerts, L.F. Santos, J. New. Phys. 11 (043026 (1), 2009)Google Scholar
  28. 28.
    L.F. Santos, J. Phys. A. 37, 4723 (2004)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    A. Gubin, L.F. Santos, Am. J. Phys. 80, 246 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    L.F. Santos, Rev. Phys. E 031125, 78 (2008)Google Scholar
  31. 31.
    L.F. Santos, J. Math. Phys. 50 (095211 (1, 2009)Google Scholar
  32. 32.
    T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, S.S.M. Wong, Rev. Mod. Phys. 53, 385 (1981)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    V.K.B. Kota, Phys. Rep. 347, 223 (2001)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    L.F. Santos, F. Borgonovi, F.M. Izrailev, Phys. Rev. E 036209, 85 (2012)Google Scholar
  35. 35.
    P.R. Zangara, A.D. Dente, E.J. Torres-Herrera, H.M. Pastawski, A. Iucci, L.F. Santos, Phys. Rev. E 032913, 88 (2013)Google Scholar
  36. 36.
    V. Zelevinsky, B.A. Brown, N. Frazier, M. Horoi, Phys. Rep. 276, 85 (1996)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    L. Mandelstam, I. Tamm, J. Phys. USSR. 9, 249 (1945)MathSciNetGoogle Scholar
  38. 38.
    I. Ersak, Sov. J. Nucl. Phys. 9, 263 (1969)Google Scholar
  39. 39.
    G.N. Fleming, Il Nuovo Cimento. 16, 232 (1973)MathSciNetCrossRefGoogle Scholar
  40. 40.
    K. Bhattacharyya, J. Phys. A. 16, 2993 (1983)ADSCrossRefGoogle Scholar
  41. 41.
    E.A. Gislason, N.H. Sabelli, J.W. Wood, Phys. Rev. A 31, 2078 (1985)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    L. Vaidman, Am. J. Phys. 60, 182 (1992)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    J. Ufink, Am. J. Phys. 61, 935 (1993)ADSCrossRefGoogle Scholar
  44. 44.
    P. Pfeifer, Rev, Phys. Lett. 70, 3365 (1993)CrossRefGoogle Scholar
  45. 45.
    V. Giovannetti, S. Lloyd, L. Maccone, Phys. Rev. A 052109, 67 (2003)Google Scholar
  46. 46.
    T.B. Boykin, N. Kharche, G. Klimeck, Eur. J. Phys. 28, 673 (2007)CrossRefGoogle Scholar
  47. 47.
    P.W. Anderson, Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  48. 48.
    B. Kramer, A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993)ADSCrossRefGoogle Scholar
  49. 49.
    F. Evers, A.D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008)ADSCrossRefGoogle Scholar
  50. 50.
    F. Izrailev, A. Krokhin, N. Makarov, Phys. Rep. 512(3), 125 (2012). Anomalous localization in low-dimensional systems with correlated disorderADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    W. Morong, B. DeMarco, arXiv:1505.01836
  52. 52.
    L. Fleishman, P.W. Anderson, Phys. Rev. B 21, 2366 (1980)ADSCrossRefGoogle Scholar
  53. 53.
    I.V. Gornyi, A.D. Mirlin, D.G. Polyakov, Phys. Rev. Lett. 206603, 95 (2005)Google Scholar
  54. 54.
    D.M. Basko, I.L. Aleiner, B.L. Altshuler, Ann. Phys. 321, 1126 (2006)ADSCrossRefGoogle Scholar
  55. 55.
    J.Z. Imbrie, On many-body localization for quantum spin chains. arXiv:1403.7837
  56. 56.
    B. Bauer, T. Schweigler, T. Langen, J. Schmiedmayer, Does an isolated quantum system relax? arXiv:1504.04288
  57. 57.
    B. Huckestein, R. Klesse, Phys. Rev. B 55, R7303 (1997)ADSCrossRefGoogle Scholar
  58. 58.
    R. Ketzmerick, G. Petschel, T. Geisel, Phys. Rev. Lett. 69, 695 (1992)ADSCrossRefGoogle Scholar
  59. 59.
    B. Huckestein, L. Schweitzer, Phys. Rev. Lett. 72, 713 (1994)ADSCrossRefGoogle Scholar
  60. 60.
    E. Cuevas, V.E. Kravtsov, Phys. Rev. B 235119, 76 (2007)Google Scholar
  61. 61.
    B. Huckestein, R. Klesse, Phys. Rev. B 59, 9714 (1999)ADSCrossRefGoogle Scholar
  62. 62.
    V.E. Kravtsov, A. Ossipov, O.M. Yevtushenko, J. Phys. A Math. Theor. 305003, 44 (2011)Google Scholar
  63. 63.
    J.T. Chalker, G.J. Daniell, Phys. Rev. Lett. 61, 593 (1988)ADSCrossRefGoogle Scholar

Copyright information

© Sociedade Brasileira de Física 2015

Authors and Affiliations

  1. 1.Instituto de Física, Universidad Autónoma de PueblaPueblaMexico
  2. 2.Department of PhysicsYeshiva UniversityNew YorkUSA
  3. 3.ITAMPHarvard-Smithsonian Center for AstrophysicsCambridgeUSA

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