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Freed by interaction kinetic states in the Harper model

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Abstract

We study the problem of two interacting particles in a one-dimensional quasiperiodic lattice of the Harper model. We show that a short or long range interaction between particles leads to emergence of delocalized pairs in the non-interacting localized phase. The properties of these freed by interaction kinetic states (FIKS) are analyzed numerically including the advanced Arnoldi method. We find that the number of sites populated by FIKS pairs grows algebraically with the system size with the maximal exponent b = 1, up to a largest lattice size N = 10 946 reached in our numerical simulations, thus corresponding to a complete delocalization of pairs. For delocalized FIKS pairs the spectral properties of such quasiperiodic operators represent a deep mathematical problem. We argue that FIKS pairs can be detected in the framework of recent cold atom experiments [M. Schreiber et al., Science 349, 842 (2015)] by a simple setup modification. We also discuss possible implications of FIKS pairs for electron transport in the regime of charge-density wave and high T c superconductivity.

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References

  1. P.G. Harper, Proc. Phys. Soc. London Sect. A 68, 874 (1955)

    Article  ADS  MATH  Google Scholar 

  2. M.Y. Azbel, Sov. Phys. J. Exp. Theor. Phys. 19, 634 (1964)

    Google Scholar 

  3. D.R. Hofstadter, Phys. Rev. B 14, 2239 (1976)

    Article  ADS  Google Scholar 

  4. S. Aubry, G. André, Ann. Israel Phys. Soc. 3, 133 (1980)

    Google Scholar 

  5. S.Y. Jitomirskaya, Ann. Math. 150, 1159 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  6. J.B. Sokoloff, Phys. Rep. 126, 189 (1985)

    Article  ADS  Google Scholar 

  7. T. Geisel, R. Ketzmerick, G. Petschel, Phys. Rev. Lett. 66, 1651 (1991)

    Article  ADS  Google Scholar 

  8. M. Wilkinson, E.J. Austin, Phys. Rev. B 50, 1420 (1994)

    Article  ADS  Google Scholar 

  9. D.L. Shepelyansky, Phys. Rev. B 54, 14896 (1996)

    Article  ADS  Google Scholar 

  10. A. Barelli, J. Bellissard, Ph. Jacquod, D.L. Shepelyansky, Phys. Rev. Lett. 77, 4752 (1996)

    Article  ADS  Google Scholar 

  11. G. Dufour, G. Orso, Phys. Rev. Lett. 109, 155306 (2012)

    Article  ADS  Google Scholar 

  12. D.L. Shepelyansky, Phys. Rev. Lett. 73, 2607 (1994)

    Article  ADS  Google Scholar 

  13. Y. Imry, Europhys. Lett. 30, 405 (1995)

    Article  ADS  Google Scholar 

  14. D. Weinmann, A. Müller–Groeling, J.-L. Pichard, K. Frahm, Phys. Rev. Lett. 75, 1598 (1995)

    Article  ADS  Google Scholar 

  15. K. Frahm, A. Müller-Groeling, J.-L. Pichard, D. Weinmann, Europhys. Lett. 31, 169 (1995)

    Article  ADS  Google Scholar 

  16. F. von Oppen, T. Wetting, J. Müller, Phys. Rev. Lett. 76, 491 (1996)

    Article  ADS  Google Scholar 

  17. K.M. Frahm, Eur. Phys. J. B 10, 371 (1999)

    Article  ADS  Google Scholar 

  18. S. Flach, M. Ivanchenko, R. Khomeriki, Europhys. Lett. 98, 66002 (2012)

    Article  ADS  Google Scholar 

  19. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature 453, 895 (2008)

    Article  ADS  Google Scholar 

  20. E. Lucioni, B. Deissler, L. Tanzi, G. Roati, M. Zaccanti, M. Modugno, M. Larcher, F. Dalfovo, M. Inguscio, G. Modugno, Phys. Rev. Lett. 106, 230403 (2011)

    Article  ADS  Google Scholar 

  21. M. Schreiber, S.S. Hodgman, P. Bordia, H. Lüschen, M.H. Fischer, R. Vosk, E. Altman, U. Schneider, I. Bloch, Science 349, 842 (2015)

    Article  ADS  Google Scholar 

  22. W.E. Arnoldi, Quart. Appl. Math. 9, 17 (1951)

    MathSciNet  MATH  Google Scholar 

  23. G.W. Stewart, Matrix Algorithms Volume II: Eigensystems (SIAM, 2001)

  24. K.M. Frahm, D.L. Shepelyansky, Eur. Phys. J. B 76, 57 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. M. Frigo, A Fast Fourier Transform Compiler, in Proc. 1999 ACM SIGPLAN Conf. “Programming Language Design and Implementation (PLDI ’99)”, Atlanta, Georgia, http://www.fftw.org/pldi99.pdf

  26. R. Lima, D.L. Shepelyansky, Phys. Rev. Lett. 67, 1377 (1991)

    Article  ADS  Google Scholar 

  27. R. Ketzmerick, K. Kruse, T. Geisel, Physica D 131, 247 (1999)

    Article  ADS  MATH  Google Scholar 

  28. T. Prosen, I.I. Satija, N. Shah, Phys. Rev. Lett. 87, 066601 (2001)

    Article  ADS  Google Scholar 

  29. R. Artuso, Scholarpedia 6, 10462 (2011)

    Article  ADS  Google Scholar 

  30. B. Chirikov, D.L. Shepelyansky, Scholarpedia 3, 3550 (2008)

    Article  ADS  Google Scholar 

  31. J. Bourgain, S. Jitomirskaya, Invent. Math. 148, 453 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. S. Jitomirskaya, C.A. Marx, arXiv:1503.05740 (2015)

  33. The Physics of Organic Superconductors and Conductors, edited by A. Lebed (Springer-Verlag, Berlin, 2008)

  34. E. Fradkin, S. Kivelson, Nat. Phys. 8, 865 (2012)

    Article  Google Scholar 

  35. B. Keimer, S.A. Kivelson, M.R. Norman, S. Uchida, J. Zaanen, Nature 518, 179 (2015)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062, Toulouse, France

    Klaus M. Frahm & Dima L. Shepelyansky

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  1. Klaus M. Frahm
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  2. Dima L. Shepelyansky
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Correspondence to Dima L. Shepelyansky.

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Frahm, K., Shepelyansky, D. Freed by interaction kinetic states in the Harper model. Eur. Phys. J. B 88, 337 (2015). https://doi.org/10.1140/epjb/e2015-60733-9

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  • DOI: https://doi.org/10.1140/epjb/e2015-60733-9

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