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Radial distribution function in a diffusion Monte Carlo simulation of a Fermion fluid between the ideal gas and the Jellium model

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Abstract

We study, through the diffusion Monte Carlo method, a spin one-half fermion fluid, in the three dimensional Euclidean space, at zero temperature. The point particles, immersed in a uniform “neutralizing” background, interact with a pair-potential which can be continuously changed from zero to the Coulomb potential depending on a parameter μ. We determine the radial distribution functions of the system for various values of density, μ, and polarization. We discuss about the importance, in a computer experiment, of the choice of suitable estimators to measure a physical quantity. The radial distribution function is determined through the usual histrogram estimator and through an estimator determined via the use of the Hellmann and Feynman theorem. In a diffusion Monte Carlo simulation the latter route introduces a new bias to the measure of the radial distribution function due to the choice of the auxiliary function. This bias is independent from the usual one due to the choice of the trial wavefunction. A brief account of the results from this study were presented in a recent communication [R. Fantoni, Solid State Commun. 159, 106 (2013)].

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References

  1. N.W. Ashcroft, N.D. Mermin, Solid State Physics (Harcourt, Inc., Forth Worth, 1976)

  2. S.L. Shapiro, S.A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars. The Physics of Compact Objects (John Wiley-VCH Verlag GmbH, Weinheim, 1983)

  3. W. Zhu, J. Toulouse, A. Savin, G. Angyan, J. Chem. Phys. 132, 244108 (2010)

    Article  ADS  Google Scholar 

  4. J. Toulouse, P. Gori-Giorgi, A. Savin, Theor. Chem. Acc. 114, 305 (2005)

    Article  Google Scholar 

  5. P. Gori-Giorgi, A. Savin, Phys. Rev. A 3, 032506 (2006)

    Article  ADS  Google Scholar 

  6. D.M. Ceperley, Rev. Mod. Phys. 67, 279 (1995)

    Article  ADS  Google Scholar 

  7. D.M. Ceperley, in Monte Carlo and Molecular Dynamics of Condensed Matter Systems, edited by K. Binder, G. Ciccotti (Editrice Compositori, Bologna, 1996)

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

    Article  ADS  Google Scholar 

  9. L. Zecca, P. Gori-Giorgi, S. Moroni, G.B. Bachelet, Phys. Rev. B 70, 205127 (2004)

    Article  ADS  Google Scholar 

  10. S. Paziani, S. Moroni, P. Gori-Giorgi, G.B. Bachelet, Phys. Rev. B 73, 155111 (2006)

    Article  ADS  Google Scholar 

  11. R. Fantoni, Solid State Commun. 159, 106 (2013)

    Article  ADS  Google Scholar 

  12. J. Kolorenc, L. Mitas, Rep. Prog. Phys. 74, 026502 (2011)

    Article  ADS  Google Scholar 

  13. W.M.C. Foulkes, L. Mitas, R.J. Needs, G. Rajagopal, Rev. Mod. Phys. 73, 33 (2001)

    Article  ADS  Google Scholar 

  14. Y. Kwon, D.M. Ceperley, R.M. Martin, Phys. Rev. B 58, 6800 (1998)

    Article  ADS  Google Scholar 

  15. J. Toulouse, R. Assaraf, C.J. Umrigar, J. Chem. Phys. 126, 244112 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. S. Chiesa, D.M. Ceperley, R.M. Martin, M. Holzmann, Phys. Rev. Lett. 97, 076404 (2006)

    Article  ADS  Google Scholar 

  18. W.L. McMillan, Phys. Rev. A 138, 442 (1965)

    ADS  Google Scholar 

  19. M.H. Kalos, D. Levesque, L. Verlet, Phys. Rev. A 9, 2178 (1974)

    Article  ADS  Google Scholar 

  20. R.W. Hockney, J.W. Eastwood, “Computer Simulation Using Particles” (McGraw-Hill, New York, 1981)

  21. M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford, 1987)

  22. D. Frenkel, B. Smit, Understanding Molecular Simulation (Academic Press, San Diego, 1996)

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

    Article  ADS  Google Scholar 

  24. D.M. Ceperley, M.H. Kalos, in Monte Carlo Methods in Statistical Physics, edited by K. Binder (Springer-Verlag, Heidelberg, 1979), p. 145

  25. K.S. Liu, M.H. Kalos, G.V. Chester, Phys. Rev. A 10, 303 (1974)

    Article  ADS  Google Scholar 

  26. R.N. Barnett, P.J. Reynolds, W.A. Lester Jr., J. Comput. Phys. 96, 258 (1991)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  27. S. Baroni, S. Moroni, Phys. Rev. Lett. 82, 4745 (1999)

    Article  ADS  Google Scholar 

  28. C.J. Umrigar, M.P. Nightingale, K.J. Runge, J. Chem. Phys. 99, 2865 (1993)

    Article  ADS  Google Scholar 

  29. R. Assaraf, M. Caffarel, J. Chem. Phys. 119, 10536 (2003)

    Article  ADS  Google Scholar 

  30. R. Gaudoin, J.M. Pitarke, Phys. Rev. Lett. 99, 126406 (2007)

    Article  ADS  Google Scholar 

  31. E. Wigner, Phys. Rev. 46, 1002 (1934)

    Article  ADS  Google Scholar 

  32. A.J. Leggett, Rev. Mod. Phys. 47, 331 (1975)

    Article  ADS  Google Scholar 

  33. G.F. Giuliani, G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2005)

  34. V. Natoli, D.M. Ceperley, Comput. Phys. 117, 171 (1995)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  35. N.H. March, M.P. Tosi, Coulomb Liquids (Academic Press, London, 1984)

  36. J.B. Anderson, J. Chem. Phys. 65, 4121 (1976)

    Article  ADS  Google Scholar 

  37. J.M. Hammersley, D.C. Handscomb, Monte Carlo Methods (Chapman and Hall, London, 1964), pp. 57–59

  38. M.H. Kalos, P.A. Whitlock, Monte Carlo Methods (Wiley-VCH Verlag GmbH & Co., Weinheim, 2008)

  39. L.D. Landau, E.M. Lifshitz, Quantum Mechanics. Non-relativistic Theory, 3rd edn. course of Theoretical Physics (Pergamon Press, 1977), Vol. 3, Eq. (11.16)

  40. A. Bijl, Physica 7, 869 (1940)

    Article  ADS  Google Scholar 

  41. R.B. Dingle, Philos. Mag. 40, 573 (1949)

    MATH  Google Scholar 

  42. R. Jastrow, Phys. Rev. 98, 1479 (1955)

    Article  MATH  ADS  Google Scholar 

  43. R.P. Feynman, Statistical Mechanics: A Set of Lectures (W.A. Benjamin Inc., London, Amsterdam, Don Mills, Sydney, Tokyo, 1972), Sect. 9.6

  44. T. Gaskell, Proc. Phys. Soc. 77, 1182 (1961)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  45. T. Gaskell, Proc. Phys. Soc. 80, 1091 (1962)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  46. D.M. Ceperley, in Proceedings of the International School of Physics Enrico Fermi, edited by G.F. Giuliani, G. Vignale (IOS Press, Amsterdam, 2004), pp. 3–42, course 158

  47. D. Ceperley, Phys. Rev. B 18, 3126 (1978)

    Article  ADS  Google Scholar 

  48. Y. Kwon, D.M. Ceperley, R.M. Martin, Phys. Rev. B 48, 12037 (1993)

    Article  ADS  Google Scholar 

  49. R.P. Feynman, M. Cohen, Phys. Rev. 102, 1189 (1956)

    Article  MATH  ADS  Google Scholar 

  50. R.M. Panoff, J. Carlson, Phys. Rev. Lett. 62, 1130 (1989)

    Article  ADS  Google Scholar 

  51. T.L. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956)

  52. E. Feenberg, Theory of Quantum Fluids (Academic Press, New York, 1967)

  53. Ph.A. Martin, Rev. Mod. Phys. 60, 1075 (1988)

    Article  ADS  Google Scholar 

  54. J.C. Kimball, Phys. Rev. A 7, 1648 (1973)

    Article  ADS  Google Scholar 

  55. A.K. Rajagopal, J.C. Kimball, M. Banerjee, Phys. Rev. B 18, 2339 (1978)

    Article  ADS  Google Scholar 

  56. M. Hoffmann-Ostenhof, T. Hofmann-Ostenhof, H. Stremnitzer, Phys. Rev. Lett. 68, 3857 (1992).

    Article  ADS  Google Scholar 

  57. J.P. Hansen, I.R. McDonald, Theory of simple liquids, 2nd edn. (Academic Press, London, 1986)

  58. L. van Hove, Phys. Rev. 95, 249 (1954)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  59. D. Pines, P. Nozières, Theory of Quantum Liquids (Benjamin, New York, 1966)

  60. J. Lindhard, Mat.-Fys. Medd. 28 (1954)

  61. M.P. Tosi, in Electron Correlation in the Solid State, edited by N.H. March (Imperial College Press, London, 1999), Chap. 1, pp. 1–42

  62. A. Alastuey, Ph.A. Martin, J. Stat. Phys. 39, 405 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  63. M.J. Lighthill, Introduction to Fourier Analysis and Generalized Functions (Cambridge University Press, 1959), Theorem 19

  64. G. Ortiz, P. Ballone, Phys. Rev. B 50, 1391 (1994)

    Article  ADS  Google Scholar 

  65. M. Kac, Probability and Related Topics in Physical Sciences (Interscience Publisher Inc., New York, 1959)

  66. M. Kac, in Proceedings of the Second Berkeley Symposium on Probability and Statistics (University of California Press, Berkeley, 1951), Sect. 3

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  1. Dipartimento di Scienze dei Materiali e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S. Marta DD2137, 30123, Venezia, Italy

    Riccardo Fantoni

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Correspondence to Riccardo Fantoni.

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Fantoni, R. Radial distribution function in a diffusion Monte Carlo simulation of a Fermion fluid between the ideal gas and the Jellium model. Eur. Phys. J. B 86, 286 (2013). https://doi.org/10.1140/epjb/e2013-40204-3

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  • DOI: https://doi.org/10.1140/epjb/e2013-40204-3

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