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One- and two-particle problem with correlated disorder potential

  • Regular Article - Solid State and Materials
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Abstract

Motivated by the recent experimental and theoretical progresses in the exploration of the effect of disorder in interacting system, we examine the effect of two types of correlated disorder, the quasi-periodic potential and speckle disorder potential, on one- and two-particle problem with exact diagonalization (ED) method. We give the phase diagram for single particle in the presence of quasi-periodic potential and also analyse the effect of strong interaction on the phase diagram for ground state in two dimensions. For the speckle disorder potential case, we examine both the effect of correlation length and disorder strength on single particle ground state energy and two-particle binding energy. Comparison of certain results between these two correlated disorder is also discussed. The transport property for different interaction strength under speckle disorder potential is also calculated and discussed at last.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The datasets generated and analyzed during the current study are not publicly available but are available from the corresponding author on reasonable request.]

References

  1. E. Abrahams (ed.), 50 Years of Anderson Localization (World Scientific, Singapore, 2010)

    MATH  Google Scholar 

  2. V. Dobrosavljevic, N. Trivedi, J. Valles, M, Conductor–Insulator Quantum Phase Transition (Oxford University Press, 2012)

  3. Sheng Ping, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, London, 1995)

    Google Scholar 

  4. Datta Supriyo, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  5. P. Anderson, W Phys. Rev. 109, 1492 (1958)

    Article  ADS  Google Scholar 

  6. E. Abrahams, P.W. Anderson, D.C. Licciardello, T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979)

    Article  ADS  Google Scholar 

  7. D.S. Wiersma, P. Bartolini, A. Lagendijk, Righini Roberto, Nature 390, 671 (1997)

    Article  ADS  Google Scholar 

  8. T. Schwartz, G. Bartal, S. Fishman, M. Segev, Nature 446, 52 (2007)

    Article  ADS  Google Scholar 

  9. R. Dalichaouch, J.P. Armstrong, S. Schultz, P.M. Platzman, S.L. McCall, Nature 354, 53 (1991)

    Article  ADS  Google Scholar 

  10. R.L. Weaver, Wave Motion 12, 129 (1990)

    Article  Google Scholar 

  11. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, A. Aspect, Nature 453, 891 (2008)

    Article  ADS  Google Scholar 

  12. 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 

  13. S.S. Kondov, W.R. McGehee, J.J. Zirbel, B. DeMarco, Science 334, 66 (2011)

    Article  ADS  Google Scholar 

  14. F. Jendrzejewski, A. Bernard, K. Muller, P. Cheinet, V. Josse, M. Piraud, L. Pezze, L. Sanchez-Palencia, A. Aspect, P. Bouyer, Nat. Phys. 8, 398 (2012)

    Article  Google Scholar 

  15. J.C. Flores, J. Phys. Condens. Matter 1, 8471 (1989)

    Article  ADS  Google Scholar 

  16. D.H. Dunlap, H.-L. Wu, P.W. Phillips, Phys. Rev. Lett. 65, 88 (1990)

    Article  ADS  Google Scholar 

  17. P. Phillips, H.-L. Wu, Science 252, 1805 (1991)

    Article  ADS  Google Scholar 

  18. P. Lugan, A. Aspect, L. Sanchez-Palencia, D. Delande, B. Grémaud, C.A. Müller, C. Miniatura, Phys. Rev. A 80, 023605 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  20. J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P.W. Hess, P. Hauke, M. Heyl, D.A. Huse, C. Monroe, Nat. Phys. 12, 907 (2016)

    Article  Google Scholar 

  21. P. Bordia, H.P. Lüschen, S.S. Hodgman, M. Schreiber, I. Bloch, U. Schneider, Phys. Rev. Lett. 116, 140401 (2016)

    Article  ADS  Google Scholar 

  22. J.-Y. Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio-Abadal, T. Yefsah, V. Khemani, D.A. Huse, I. Bloch, C. Gross, Science 352, 1547 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  23. P. Bordia, H. Lüschen, S. Scherg, S. Gopalakrishnan, M. Knap, U. Schneider, I. Bloch, Phys. Rev. X 7, 041047 (2017)

    Google Scholar 

  24. J.-P. Brantut, J. Meineke, D. Stadler, S. Krinner, T. Esslinger, Science 337, 1069 (2012)

    Article  ADS  Google Scholar 

  25. D. Stadler, S. Krinner, J. Meineke, J.-P. Brantut, T. Esslinger, Nature 491, 736 (2012)

    Article  ADS  Google Scholar 

  26. S. Krinner, D. Stadler, J. Meineke, J.-P. Brantut, T. Esslinger, Phys. Rev. Lett. 110, 100601 (2013)

    Article  ADS  Google Scholar 

  27. S. Krinner, D. Stadler, J. Meineke, J.-P. Brantut, T. Esslinger, Phys. Rev. Lett. 115, 045302 (2015)

    Article  ADS  Google Scholar 

  28. Jérémie Richard, Lih-King Lim, Vincent Denechaud, Valentin V. Volchkov, Baptiste Lecoutre, Musawwadah Mukhtar, Fred Jendrzejewski, Alain Aspect, Adrien Signoles, Laurent Sanchez-Palencia, VincentLim Josse, Phys. Rev. Lett 122, 100403 (2019)

    Article  ADS  Google Scholar 

  29. P.G. Harper, Proc. Phys. Soc. Lond. A 68, 874 (1955)

    Article  ADS  Google Scholar 

  30. Aubry, G. André, Ann. Isr. Phys. Soc. 3, 33 (1980)

    Google Scholar 

  31. J.W. Goodman, Speckle Phenomena in Optics: Theory and Applications, Chapter 2 (Roberts and Company Publishers, Greenwood Village, 2007)

    Google Scholar 

  32. J.M. Huntley, Appl. Opt. 28, 20 (1989)

    Google Scholar 

  33. H. Fehske, R. Schneider, A. Weiße (eds.), Computational Many-Particle Physics, Chapter 18 (Springer, Berlin, 2008)

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. B. Georgeot, D.L. Shepelyansky, Phys. Rev. Lett. 79, 4365 (1997)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Pere Mujal, Artur Polls, Sebastiano Pilati, Bruno Juliá-Díaz, Phys. Rev. A 100, 013603 (2019)

    Article  ADS  Google Scholar 

  43. M. Filippone, P.W. Brouwer, J. Eisert, F. von Oppen, Phys. Rev. B 94, 201112 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. B.I. Shklovskii, Semiconductors 42, 909–913 (2008)

    Article  ADS  Google Scholar 

  46. T. Bushch, B.-G. Englert, K. Rzazewski, M. Wilkens, Found. Phys. 28, 549 (1998)

    Article  Google Scholar 

  47. W. Kohn, Phys. Rev. 133, A171 (1964)

    Article  ADS  Google Scholar 

  48. B.S. Shastry, B. Sutherland, Phys. Rev. Lett. 65, 243 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  49. D.J. Scalapino, S.R. White, S.-C. Zhang, Phys. Rev. Lett. 68, 2830 (1992)

    Article  ADS  Google Scholar 

  50. D.J. Scalapino, S.R. White, S.-C. Zhang, Phys. Rev. B 47, 7995 (1993)

    Article  ADS  Google Scholar 

  51. R. Kotlyar, S. Das Sarma, Phys. Rev. Lett. 86, 2388 (2001)

    Article  ADS  Google Scholar 

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Acknowledgements

The author would like to thank Zhihao Xu, Shizhong Zhang and Zhenhua Yu for useful discussions and critical reading of the manuscript. This work is supported by the Key-Area Research and Development Program of GuangDong Province under Grants No. 2019B030330001, the National Natural Science Foundation of China (NNSFC) under Grants nos. 11474179, 11722438, 91736103, 12074440 and Hong Kong Research Grants Council (General Research Fund, HKU 17318316 and Collaborative Research Fund, C6026-16W).

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Authors and Affiliations

  1. Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus), Zhuhai, 519082, China

    Guangcun Liu

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  1. Guangcun Liu
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All the authors were involved in the preparation of the manuscript. All the authors have read and approved the final manuscript.

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Correspondence to Guangcun Liu.

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Liu, G. One- and two-particle problem with correlated disorder potential. Eur. Phys. J. B 94, 12 (2021). https://doi.org/10.1140/epjb/s10051-020-00036-0

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