Journal of Low Temperature Physics

, Volume 185, Issue 1–2, pp 39–58 | Cite as

Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

  • S. Molinelli
  • D. E. Galli
  • L. Reatto
  • M. Motta


We compute several ground-state properties and the dynamical structure factor of a zero-temperature system of Bosons interacting with the 2D screened Coulomb (2D-SC) potential. We resort to the exact shadow path integral ground state (SPIGS) quantum Monte Carlo method to compute the imaginary-time correlation function of the model, and to the genetic algorithm via falsification of theories (GIFT) to retrieve the dynamical structure factor. We provide a detailed comparison of ground-state properties and collective excitations of 2D-SC and \(^4\)He atoms. The roton energy of the 2D-SC system is an increasing function of density, and not a decreasing one as in \(^4\)He. This result is in contrast with the view that the roton is the soft mode of the fluid–solid transition. We uncover a remarkable quasi-universality of backflow and of other properties when expressed in terms of the amount of short-range order as quantified by the height of the first peak of the static structure factor.


Quantum liquids Soft-core interaction Dynamical properties 



It is a pleasure to dedicate this contribution to Flavio Toigo, honoring a scientist who has given important contributions in many areas of condensed matter and statistical physics. We acknowledge the CINECA and the Regione Lombardia award, under the LISA initiative, for the availability of high-performance computing resources and support. One of us (L.R.) wants to thank Dipartimento di Fisica, Università degli Studi di Milano, for some support to his research activity. One of us (M.M.) acknowledges the support from Dipartimento di Fisica, Università degli Studi di Milano, the Simons Foundation, and NSF (Grant No. DMR-1409510).


  1. 1.
    D. Pines, P. Noziéres, The Theory of Quantum Liquids: Normal Fermi Liquids (W. A. Benjamin, New York, 1966)Google Scholar
  2. 2.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971)Google Scholar
  3. 3.
    H.H. Glyde, Excitations in Liquid and Solid Helium (Clarendon Press, Oxford, 1994)Google Scholar
  4. 4.
    D.M. Ceperley, Rev. Mod. Phys. 67, 279 (1995)ADSCrossRefGoogle Scholar
  5. 5.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    M.A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, M. Rigol, Rev. Mod. Phys. 83, 1405 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    S. De Palo, S. Conti, S. Moroni, Phys. Rev. B 69, 035109 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    R. Rota, F. Tramonto, D.E. Galli, S. Giorgini, Phys. Rev. B 88, 214505 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    M.H. Kalos, M.A. Lee, P.A. Whitlock, G.V. Chester, Phys. Rev. B 24, 115 (1981)ADSCrossRefGoogle Scholar
  10. 10.
    R. Rota, F. Tramonto, D.E. Galli, S. Giorgini, J. Phys.: Conf. Ser. 529, 012022 (2014)ADSGoogle Scholar
  11. 11.
    D.R. Nelson, H.S. Seung, Phys. Rev. B 39, 9153 (1989)ADSCrossRefGoogle Scholar
  12. 12.
    G. Giuliani, G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2005)CrossRefGoogle Scholar
  13. 13.
    L. Xing, Z. Tesanovic, Phys. Rev. Lett. 65, 794 (1990)ADSCrossRefGoogle Scholar
  14. 14.
    W.R. Magro, D.M. Ceperley, Phys. Rev. B 48, 411 (1993)ADSCrossRefGoogle Scholar
  15. 15.
    M. Rossi, S.L. Zavattari, D.E. Galli, L. Reatto, Phys. Rev. B 84, 052504 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    H. Nordborg, G. Blatter, Phys. Rev. Lett. 79, 1925 (1997)ADSCrossRefGoogle Scholar
  17. 17.
    H. Nordborg, G. Blatter, Phys. Rev. B 58, 14556 (1998)ADSCrossRefGoogle Scholar
  18. 18.
    M. Boninsegni, H.R. Glyde, J. Low Temp. Phys. 112, 251 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    S. Moroni, D.E. Galli, S. Fantoni, L. Reatto, Phys. Rev. B 58, 909 (1998)ADSCrossRefGoogle Scholar
  20. 20.
    E. Vitali, M. Rossi, L. Reatto, D.E. Galli, Phys. Rev. B 82, 174510 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    M. Rossi, E. Vitali, L. Reatto, D.E. Galli, Phys. Rev. B 85, 014525 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    B. Fak, T. Keller, M.E. Zhitomirsky, A.L. Chernyshev, Phys. Rev. Lett. 109, 155305 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    F. Arrigoni, E. Vitali, D.E. Galli, L. Reatto, Fiz. Niz. Temp. 39, 1021 (2013)Google Scholar
  24. 24.
    L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003)MATHGoogle Scholar
  25. 25.
    R.N. Silver, D.S. Sivia, J.E. Gubernatis, M. Jarrell, Phys. Rev. Lett. 65, 496 (1990)ADSCrossRefGoogle Scholar
  26. 26.
    M. Jarrell, J.E. Gubernatis, Phys. Rep. 269, 133 (1996)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    S.R. White, Computer Simulation Studies in Condensed Matter Physics (Springer, Berlin, 1991)Google Scholar
  28. 28.
    M. Boninsegni, D.M. Ceperley, J. Low Temp. Phys. 104, 339 (1996)ADSCrossRefGoogle Scholar
  29. 29.
    M. Nava, D.E. Galli, S. Moroni, E. Vitali, Phys. Rev. B 87, 144506 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    M. Motta, D.E. Galli, S. Moroni, E. Vitali, J. Chem. Phys. 140, 024107 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    M. Motta, D.E. Galli, S. Moroni, E. Vitali, J. Chem. Phys. 143, 164108 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    D.E. Galli, L. Reatto, Mol. Phys. 101, 1697 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    D.E. Galli, L. Reatto, J. Low Temp. Phys. 136, 343 (2004)ADSCrossRefGoogle Scholar
  34. 34.
    A. Sarsa, K.E. Schmidt, W.R. Magro, J. Chem. Phys. 113, 1366 (2000)ADSCrossRefGoogle Scholar
  35. 35.
    E.L. Pollock, D.M. Ceperley, Phys. Rev. B 30, 2555 (1984)ADSCrossRefGoogle Scholar
  36. 36.
    Y. Yan, D. Blume, Phys. Rev. A 91, 043607 (2015)ADSCrossRefGoogle Scholar
  37. 37.
    N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)ADSCrossRefGoogle Scholar
  38. 38.
    M. Rossi, M. Nava, L. Reatto, D.E. Galli, J. Chem. Phys. 131, 154108 (2009)ADSCrossRefGoogle Scholar
  39. 39.
    S.A. Vitiello, K. Runge, M.H. Kalos, Phys. Rev. Lett. 60, 1970 (1988)ADSCrossRefGoogle Scholar
  40. 40.
    L. Reatto, G.L. Masserini, Phys. Rev. B 38, 4516 (1988)ADSCrossRefGoogle Scholar
  41. 41.
    S.A. Vitiello, K.J. Runge, G.V. Chester, M.H. Kalos, Phys. Rev. B 42, 228 (1990)ADSCrossRefGoogle Scholar
  42. 42.
    T. MacFarland, S.A. Vitiello, L. Reatto, G.V. Chester, M.H. Kalos, Phys. Rev. B 50, 13577 (1994)ADSCrossRefGoogle Scholar
  43. 43.
    M. Caffarel, P. Claverie, J. Stat. Phys. 43, 797 (1986)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    M. Holzmann, D.M. Ceperley, C. Pierleoni, K. Esler, Phys. Rev. E 68, 046707 (2003)ADSCrossRefGoogle Scholar
  45. 45.
    M. Motta, G. Bertaina, D.E. Galli, E. Vitali, Comp. Phys. Comm. 190, 62 (2015)ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    A.N. Tikhonov, V.Y. Arsenin, Solution of Ill-Posed Problems (Winston & Sons, New York, 1977)MATHGoogle Scholar
  47. 47.
    A. Tarantola, Nat. Phys. 2, 492 (2006)CrossRefGoogle Scholar
  48. 48.
    A.W. Sandvik, Phys. Rev B 57, 10287 (1998)ADSCrossRefGoogle Scholar
  49. 49.
    M. Jarrell, in Lectures on the Physics of strongly correlated systems XII, ed. A. Avella and F. Mancini, American Institute of Physics (2008)Google Scholar
  50. 50.
    A.S. Mishchenko, in Correlated electrons: from models to materials, modeling and simulation, ed. E. Pavarini, E. Koch, F. Anders and M. Jarrell, Forschungszentrum Jülich (2012)Google Scholar
  51. 51.
    G. Bertaina, M. Motta, M. Rossi, E. Vitali, D.E. Galli, Phys. Rev. Lett. 116, 135302 (2016)ADSCrossRefGoogle Scholar
  52. 52.
    S.L. Zavattari, Quantum Monte Carlo study of 2D Yukawa Boson systems, M.D. Thesis, Universita’ degli Studi di Milano (2008)Google Scholar
  53. 53.
    T. Schneider, C.P. Enz, Phys. Rev. Lett. 27, 1186 (1971)ADSCrossRefGoogle Scholar
  54. 54.
    P. Nozières, J. Low Temp. Phys. 137, 45 (2004)ADSCrossRefGoogle Scholar
  55. 55.
    R.P. Feynman, M. Cohen, Phys. Rev. 102, 1189 (1956)ADSCrossRefGoogle Scholar
  56. 56.
    D. Hall, E. Feenberg, Ann. Phys. (NY) 63, 335 (1971)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • S. Molinelli
    • 1
  • D. E. Galli
    • 1
  • L. Reatto
    • 2
  • M. Motta
    • 3
  1. 1.Dipartimento di FisicaUniversità degli Studi di MilanoMilanoItaly
  2. 2.MilanoItaly
  3. 3.Department of PhysicsThe College of William and MaryWilliamsburgUSA

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