Melting a Hubbard dimer: benchmarks of ‘ALDA’ for quantum thermodynamics

Abstract

The competition between evolution time, interaction strength, and temperature challenges our understanding of many-body quantum systems out-of-equilibrium. Here, we consider a benchmark system, the Hubbard dimer, which allows us to explore all the relevant regimes and calculate exactly the related average quantum work. At difference with previous studies, we focus on the effect of increasing temperature, and show how this can turn the competition between many-body interactions and driving field into synergy. We then turn to use recently proposed protocols inspired by density functional theory to explore if these effects could be reproduced by using simple approximations. We find that, up to and including intermediate temperatures, a method which borrows from ground-state adiabatic local density approximation improves dramatically the estimate for the average quantum work, including, in the adiabatic regime, when correlations are strong. However at high temperature and at least when based on the pseudo-LDA, this method fails to capture the counterintuitive qualitative dependence of the quantum work with interaction strength, albeit getting the quantitative estimates relatively close to the exact results.

References

  1. 1.

    W. Yang, P. Mori-Sanchez, A.J. Cohen, AIP Conf. Proc. 1504, 605 (2012)

    ADS  Google Scholar 

  2. 2.

    K. Burke, J. Chem. Phys. 136. 150901 (2012)

    ADS  Google Scholar 

  3. 3.

    J.P. Perdew, MRS Bull. 38, 743 (2013)

    Google Scholar 

  4. 4.

    R.O. Jones, Rev. Mod. Phys. 87, 897 (2015)

    ADS  Google Scholar 

  5. 5.

    H.S. Yu, S.L. Li, D.G. Truhlar, J. Chem. Phys. 145, 130901 (2016)

    ADS  Google Scholar 

  6. 6.

    E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52, 997 (1984)

    ADS  Google Scholar 

  7. 7.

    K. Burke, J. Werschnik, E.K.U. Gross, J. Chem. Phys. 123, 062206 (2005)

    ADS  Google Scholar 

  8. 8.

    M.E. Casida, M. Huix-Rotllant, Annu. Rev. Phys. Chem. 63, 287 (2012)

    ADS  Google Scholar 

  9. 9.

    C.A. Ullrich,Time-Dependent Density-Functional Theory: Concepts and Applications, (OUP, Oxford, 2011)

  10. 10.

    S. Kurth, G. Stefanucci, C.-O. Almbladh, A. Rubio, E.K.U. Gross, Phys. Rev. B 72, 035308 (2005)

    ADS  Google Scholar 

  11. 11.

    D. Karlsson, A. Privitera, C. Verdozzi, Phys. Rev. Lett. 106, 116401 (2011)

    ADS  Google Scholar 

  12. 12.

    M. Brandbyge, J. Mozos, P. Ordejón, J. Taylor, K. Stokbro, Phys. Rev. B 65, 165401 (2002)

    ADS  Google Scholar 

  13. 13.

    J.C. Smith, F. Sagredo, K. Burke, inWarming Up Density Functional Theory, (Springer Singapore, Singapore, 2018) p. 249

  14. 14.

    M. Herrera, R.M. Serra, I. D’Amico, Sci. Rep. 7, 4655 (2017)

    ADS  Google Scholar 

  15. 15.

    A. Pribram-Jones, P.E. Grabowski, K. Burke, Phys. Rev. Lett. 116, 233001 (2016)

    ADS  Google Scholar 

  16. 16.

    J. Goold, M. Huber, A. Riera, L. del Rio, P. Skrzypczyk, J. Phys. A: Math. Theor. 49, 143001 (2016)

    ADS  Google Scholar 

  17. 17.

    S. Vinjanampathy, J. Anders, Contemp. Phys. 57, 545 (2016)

    ADS  Google Scholar 

  18. 18.

    J. Millen, A. Xuereb, New J. Phys. 18, 011002 (2016)

    ADS  Google Scholar 

  19. 19.

    J.M.R. Parrondo, J.M. Horowitz, T. Sagawa, Nat. Phys. 11, 131 (2015)

    Google Scholar 

  20. 20.

    D. Girolami, R. Schmidt, G. Adesso, Ann. Phys. 527, 757 (2015)

    MathSciNet  Google Scholar 

  21. 21.

    D. Castelvecchi, Nature 543, 597 (2017)

    ADS  Google Scholar 

  22. 22.

    C. Bustamante, J. Liphardt, F. Ritort, Phys. Today 58, 43 (2005)

    Google Scholar 

  23. 23.

    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. 113, 140601 (2014)

    ADS  Google Scholar 

  24. 24.

    S. An, J.-N. Zhang, M. Um, D. Lv, Y. Lu, J. Zhang, Z.-Q. Yin, H.T. Quan, K. Kim, Nat. Phys. 11, 193 (2014)

    Google Scholar 

  25. 25.

    T. Batalhão, A.M. Souza, R.S. Sarthour, I.S. Oliveira, M. Paternostro, E. Lutz, R.M. Serra, Phys. Rev. Lett. 115, 190601 (2015)

    ADS  Google Scholar 

  26. 26.

    J.P.S. Peterson, R.S. Sarthour, A.M. Souza, I.S. Oliveira, J. Goold, K. Modi, D.O. Soares-Pinto, L.C. Céleri, Proc. R. Soc. A 472, 20150813 (2016)

    ADS  Google Scholar 

  27. 27.

    P.A. Camati, J.P.S. Peterson, T.B. Batalhão, K. Micadei, A.M. Souza, R.S. Sarthour, I.S. Oliveira, R.M. Serra, Phys. Rev. Lett. 117, 240502 (2016)

    ADS  Google Scholar 

  28. 28.

    K. Micadei, J.P.S. Peterson, A.M. Souza, R.S. Sarthour, I.S. Oliveira, G.T. Landi, T.B. Batalhão, R.M. Serra, E.Lutz, Reversing the thermodynamic arrow of time using quantum correlations, https://doi.org/arXiv:1711.03323v1 (2017)

  29. 29.

    A. Silva, Phys. Rev. Lett. 101, 120603 (2008)

    ADS  Google Scholar 

  30. 30.

    E. Mascarenhas, H. Bragança, R. Dorner, M.F. Santos, V. Vedral, K. Modi, J. Goold, Phys. Rev. E, 89, 062103 (2014)

    ADS  Google Scholar 

  31. 31.

    L. Fusco, S. Pigeon, T.J.G. Apollaro, A. Xuereb, L. Mazzola, M. Campisi, A. Ferraro, M. Paternostro, G. De Chiara, Phys. Rev. X 4, 031029 (2014)

    Google Scholar 

  32. 32.

    M. Zhong, P. Tong, Phys. Rev. E 91, 032137 (2015)

    ADS  Google Scholar 

  33. 33.

    J. Eisert, M. Friesdorf, C. Gogolin, Nat. Phys. 11, 124 (2015)

    Google Scholar 

  34. 34.

    A. Leonard, S. Deffner, Chem. Phys. 446, 18 (2015)

    Google Scholar 

  35. 35.

    E. Solano-Carrillo, A.J. Millis, Phys. Rev. B 93, 224305 (2016)

    ADS  Google Scholar 

  36. 36.

    D.J. Carrascal, J. Ferrer, J.C. Smith, K. Burke, J. Phys. Condens. Matter: 27, 393001 (2015)

    Google Scholar 

  37. 37.

    J.I. Fuks, N.T. Maitra, Phys. Chem. Chem. Phys. 16, 14504 (2014)

    Google Scholar 

  38. 38.

    J.P. Coe, V.V. França, I. D’Amico, Phys. Rev. A 81, 052321 (2010)

    ADS  Google Scholar 

  39. 39.

    K. Kikoin, M. Kiselev, Y. Avishai.Dynamical Symmetries for Nanostructures. (Springer-Verlag, Wien, 2012)

    Google Scholar 

  40. 40.

    P. Barthelemy, L.M.K. Vandersypen, Ann. Phys. 525, 808 (2013)

    MathSciNet  Google Scholar 

  41. 41.

    S. Murmann, A. Bergschneider, V.M. Klinkhamer, G. Zürn, T. Lompe, S. Jochim, Phys. Rev. Lett. 114, 080402 (2015)

    ADS  Google Scholar 

  42. 42.

    P. Talkner, E. Lutz, P. Hänggi, Phys. Rev. E 75, 050102 (2007)

    ADS  Google Scholar 

  43. 43.

    J.P. Coe, A. Sudbery, I. Damico, Phys. Rev. B 77, 205122 (2008)

    ADS  Google Scholar 

  44. 44.

    W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965)

    ADS  Google Scholar 

  45. 45.

    K. Capelle, V.L. Campo, Phys. Rep. 528, 91 (2013)

    ADS  MathSciNet  Google Scholar 

  46. 46.

    N.A. Lima, M.F. Silva, L.N. Oliveira, K. Capelle, Phys. Rev. Lett. 90, 146402 (2003)

    ADS  Google Scholar 

Download references

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Correspondence to Irene D’Amico.

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Contribution to the Topical Issue ”Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.

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Herrera, M., Zawadzki, K. & D’Amico, I. Melting a Hubbard dimer: benchmarks of ‘ALDA’ for quantum thermodynamics. Eur. Phys. J. B 91, 248 (2018). https://doi.org/10.1140/epjb/e2018-90186-5

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