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Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena

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Abstract

We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices (OLs) computed via density functional theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus is on a half-filled one-dimensional OLs, for which the DMC simulations performed within the fixed-node approach provide unbiased results. This allows us to demonstrate that the local spin-density approximation (LSDA) to the exchange-correlation functional of DFT is very accurate in the weak and intermediate interactions regime, and also to underline its limitations close to the strongly-interacting Tonks–Girardeau limit and in very deep OLs. We also consider a three-dimensional OL at quarter filling, showing also in this case the high accuracy of the LSDA in the moderate interaction regime. The one-dimensional data provided in this study may represent a useful benchmark to further develop DFT methods beyond the LSDA and they will hopefully motivate experimental studies to accurately measure the equation of state of Fermi gases in higher-dimensional geometries.

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References

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

    Article  ADS  Google Scholar 

  2. R.G. Parr, W. Yang, Density-functional theory of atoms and molecules (Oxford University Press, New York, 1989)

  3. W. Kohn, A.D. Becke, R.G. Parr, J. Phys. Chem. 100, 12974 (1996)

    Article  Google Scholar 

  4. J.P. Perdew, K. Schmidt, Jacob’s ladder of density functional approximations for the exchange-correlation energy, in AIP Conference Proceedings (AIP, 2001), Vol. 577, pp. 1–20

  5. J. Tao, J.P. Perdew, V.N. Staroverov, G.E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003)

    Article  ADS  Google Scholar 

  6. V.N. Staroverov, G.E. Scuseria, J. Tao, J.P. Perdew, Phys. Rev. B 69, 075102 (2004)

    Article  ADS  Google Scholar 

  7. V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991)

    Article  ADS  Google Scholar 

  8. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    Article  ADS  Google Scholar 

  9. D. Jaksch, P. Zoller, Ann. Phys. (N.Y.) 315, 52 (2005)

    Article  ADS  Google Scholar 

  10. S. Pilati, I. Zintchenko, M. Troyer, Phys. Rev. Lett. 112, 015301 (2014)

    Article  ADS  Google Scholar 

  11. S. Pilati, M. Troyer, Phys. Rev. Lett. 108, 155301 (2012)

    Article  ADS  Google Scholar 

  12. F. De Soto, M. Gordillo, Phys. Rev. A 85, 013607 (2012)

    Article  ADS  Google Scholar 

  13. G. Boéris et al., Phys. Rev. A 93, 011601 (2016)

    Article  ADS  Google Scholar 

  14. G.E. Astrakharchik, K.V. Krutitsky, M. Lewenstein, F. Mazzanti, Phys. Rev. A 93, 021605 (2016)

    Article  ADS  Google Scholar 

  15. P.N. Ma, S. Pilati, M. Troyer, X. Dai, Nat. Phys. 8, 601 (2012)

    Article  Google Scholar 

  16. A. Bulgac, Y.L. Luo, P. Magierski, K.J. Roche, Y. Yu, Science 332, 1288 (2011)

    Article  ADS  Google Scholar 

  17. A. Bulgac, M.M. Forbes, M.M. Kelley, K.J. Roche, G. Wlazłowski, Phys. Rev. Lett. 112, 025301 (2014)

    Article  ADS  Google Scholar 

  18. F. Ancilotto, Phys. Rev. A 93, 053627 (2016)

    Article  ADS  Google Scholar 

  19. F. Ancilotto, Phys. Rev. A 92, 061602 (2015)

    Article  ADS  Google Scholar 

  20. I. Zintchenko, L. Wang, M. Troyer, Eur. Phys. J. B 89, 180 (2016)

    Article  ADS  Google Scholar 

  21. D.M. Ceperley, J. Stat. Phys. 63, 1237 (1991)

    Article  ADS  Google Scholar 

  22. C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010)

    Article  ADS  Google Scholar 

  23. P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. S.H. Abedinpour, M. Polini, G. Xianlong, M.P. Tosi, Phys. Rev. A 75, 015602 (2007)

    Article  ADS  Google Scholar 

  26. D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45, 566 (1980)

    Article  ADS  Google Scholar 

  27. J.P. Perdew, W. Yue, Phys. Rev. B 33, 8800 (1986)

    Article  ADS  Google Scholar 

  28. P.J. Reynolds, D.M. Ceperley, B.J. Alder, W.A. Lester Jr., J. Chem. Phys. 77, 5593 (1982)

    Article  ADS  Google Scholar 

  29. W. Foulkes, L. Mitas, R. Needs, G. Rajagopal, Rev. Mod. Phys. 73, 33 (2001)

    Article  ADS  Google Scholar 

  30. S. Pilati, G. Bertaina, S. Giorgini, M. Troyer, Phys. Rev. Lett. 105, 030405 (2010)

    Article  ADS  Google Scholar 

  31. G. Valtolina, F. Scazza, A. Amico, A. Burchianti, A. Recati, T. Enss, M. Inguscio, M. Zaccanti, G. Roati, Nat. Phys. 13, 704 (2017)

    Article  Google Scholar 

  32. A. Recati, S. Stringari, Phys. Rev. Lett. 106, 080402 (2011)

    Article  ADS  Google Scholar 

  33. M. Casula, D. Ceperley, E.J. Mueller, Phys. Rev. A 78, 033607 (2008)

    Article  ADS  Google Scholar 

  34. G.E. Astrakharchik, D. Blume, S. Giorgini, L.P. Pitaevskii, Phys. Rev. Lett. 93, 050402 (2004)

    Article  ADS  Google Scholar 

  35. N. Matveeva, G.E. Astrakharchik, New J. Phys. 18, 065009 (2016)

    Article  ADS  Google Scholar 

  36. J. Boronat, in Microscopic approaches to quantum liquids in confined geometries, edited by E. Krotscheck, J. Navarro (World Scientific, Singapore, 2002), Chap. 2, pp. 21–99

  37. M. Girardeau, J. Math. Phys. 1, 516 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  38. M.D. Girardeau, Phys. Rev. A 82, 011607 (2010)

    Article  ADS  Google Scholar 

  39. G. Zürn, F. Serwane, T. Lompe, A.N. Wenz, M.G. Ries, J.E. Bohn, S. Jochim, Phys. Rev. Lett. 108, 075303 (2012)

    Article  ADS  Google Scholar 

  40. L. Guan, S. Chen, Y. Wang, Z.Q. Ma, Phys. Rev. Lett. 102, 160402 (2009)

    Article  ADS  Google Scholar 

  41. L. Guan, S. Chen, Phys. Rev. Lett. 105, 175301 (2010)

    Article  ADS  Google Scholar 

  42. M. Olshanii, Phys. Rev. Lett. 81, 938 (1998)

    Article  ADS  Google Scholar 

  43. S. Pilati, L. Barbiero, R. Fazio, L. Dell’Anna, Phys. Rev. A 96, 021601 (2017)

    Article  ADS  Google Scholar 

  44. K. Huang, C.N. Yang, Phys. Rev. 105, 767 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  45. C. Lin, F.H. Zong, D.M. Ceperley, Phys. Rev. E 64, 016702 (2001)

    Article  ADS  Google Scholar 

  46. C.C. Chang, S. Zhang, D.M. Ceperley, Phys. Rev. A 82, 061603 (2010)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, via Marzolo 8, 35131, Padova, Italy

    Sebastiano Pilati & Francesco Ancilotto

  2. School of Science and Technology, Physics Division, University of Camerino, Via Madonna delle Carceri 9, 62032, Camerino, Italy

    Sebastiano Pilati

  3. Theoretische Physik, ETH Zurich, 8093, Zurich, Switzerland

    Ilia Zintchenko & Matthias Troyer

  4. Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA, USA

    Matthias Troyer

  5. CNR-IOM Democritos, via Bonomea 265, 34136, Trieste, Italy

    Francesco Ancilotto

Authors
  1. Sebastiano Pilati
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  2. Ilia Zintchenko
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  3. Matthias Troyer
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  4. Francesco Ancilotto
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Correspondence to Sebastiano Pilati.

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Supplementary material in the form of one pdf file available from the Journal web page at https://doi.org/10.1140/epjb/e2018-90021-1 .

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Pilati, S., Zintchenko, I., Troyer, M. et al. Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena. Eur. Phys. J. B 91, 70 (2018). https://doi.org/10.1140/epjb/e2018-90021-1

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  • DOI: https://doi.org/10.1140/epjb/e2018-90021-1

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