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Distribution of level spacing ratios using one- plus two-body random matrix ensembles

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Abstract

Probability distribution (P(r)) of the level spacing ratios has been introduced recently and is used to investigate many-body localization as well as to quantify the distance from integrability on finite size lattices. In this paper, we study the distribution of the ratio of consecutive level spacings using one-body plus two-body random matrix ensembles for finite interacting many-fermion and many-boson systems. P(r) for these ensembles move steadily from the Poisson to the Gaussian orthogonal ensemble (GOE) form as the two-body interaction strength λ is varied. Other related quantities are also used in the analysis to obtain critical strength λc for the transition. The λc values deduced using the P(r) analysis are in good agreement with the results obtained using the nearest neighbour spacing distribution (NNSD) analysis.

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References

  1. V K B Kota, Embedded random matrix ensembles in quantum physics, Lecture Notes in Physics (Springer, Heidelberg, 2014) Vol. 884

  2. F Haake, Quantum signatures of chaos, 3rd Edn (Springer-Verlag, Heidelberg, 2010)

  3. M V Berry and M Tabor, Proc. R. Soc. (London) A 356, 375 (1977)

  4. O Bohigas, M-J Giannoni and C Schmit, Phys. Rev. Lett. 52, 1 (1984)

  5. B Gremaud and S R Jain, J. Phys. A 31, L637 (1998)

  6. Z Ahmed and S R Jain, Phys. Rev. E 67, 045106 (2003); J. Phys. A 36, 3349 (2003)

  7. T A Brody, J Flores, J B French, P A Mello, A Pandey and S S M Wong, Rev. Mod. Phys. 53, 385 (1981)

  8. V Oganesyan and D A Huse, Phys. Rev. B 75, 155111 (2007)

  9. C Kollath, G Roux, G Biroli and A M Läuchli, J. Stat. Mech. P08011 (2010)

  10. M Collura, H Aufderheide, G Roux and D Karevski, Phys. Rev. A 86, 013615 (2012)

  11. N D Chavda, H N Deota and V K B Kota, Phys. Lett. A 378, 3012 (2014)

  12. V Oganesyan, A Pal and D A Huse, Phys. Rev. B 80, 115104 (2009)

  13. A Pal and D A Huse, Phys. Rev. B 82, 174411 (2010)

  14. S Iyer, V Oganesyan, G Refael and D A Huse, Phys. Rev. B 87, 134202 (2013)

  15. Y Y Atas, E Bogomolny, O Giraud and G Roux, Phys. Rev. Lett. 110, 084101 (2013)

  16. S K Haldar, B Chakrabarti, N D Chavda, T K Das, S Canuto and V K B Kota, Phys. Rev. A 89, 043607 (2014)

  17. N D Chavda and V K B Kota, Phys. Lett. A 377, 3009 (2013)

  18. V K B Kota, Phys. Rep. 347, 223 (2001)

  19. N D Chavda, V Potbhare and V K B Kota, Phys. Lett. A 311, 331 (2003)

  20. N D Chavda, V K B Kota and V Potbhare, Phys. Lett. A 376, 2972 (2012)

  21. T Asaga, L Benet, T Rupp and H A Weidenmüller, Ann. Phys. (N.Y.) 298, 229 (2002)

  22. V K B Kota, A Relaño, J Retamosa and M Vyas, J. Stat. Mech. P10028, 1 (2011)

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Acknowledgements

The author thanks V K B Kota and V Potbhare for useful discussions and also acknowledges support from the University Grants Commission, New Delhi (India) (Grant No. F.40-425/2011(SR)).

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  1. Applied Physics Department, Faculty of Technology and Engineering, Maharaja Sayajirao University of Baroda, Vadodara, 390 001, India

    N D CHAVDA

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CHAVDA, N.D. Distribution of level spacing ratios using one- plus two-body random matrix ensembles. Pramana - J Phys 84, 309–316 (2015). https://doi.org/10.1007/s12043-015-0933-8

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