Skip to main content
SpringerLink
Log in

Sum-rules and Goldstone modes from extended random phase approximation theories in Fermi systems with spontaneously broken symmetries

  • Colloquium
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

The Self-Consistent RPA (SCRPA) approach is elaborated for cases with a continuously broken symmetry, this being the main focus of the present article. Correlations beyond standard RPA are summed up correcting for the quasi-boson approximation in standard RPA. Desirable properties of standard RPA such as fulfillment of energy weighted sum rule and appearance of Goldstone (zero) modes are kept. We show theoretically and, for a model case, numerically that, indeed, SCRPA maintains all properties of standard RPA for practically all situations of spontaneously broken symmetries. A simpler approximate form of SCRPA, the so-called renormalised RPA, also has these properties. The SCRPA equations are first outlined as an eigenvalue problem, but it is also shown how an equivalent many body Green’s function approach can be formulated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Quantum Monte Carlo Methods in Physics and Chemistry, edited by M.P. Nightingale, C.J. Umrigar (Springer, Berlin, 1999)

  2. M. Holzmann, B. Bernu, C. Pierleoni, J. Mc Minis, D.M. Ceperly, V. Olevano, L. Delle Site, Phys. Rev. Lett. 107, 110402 (2011)

  3. Density-Matrix Renormalization, A New Numerical Method in Physics, edited by I. Peschel, X. Wang, M. Kaulke, K. Hallberg (Springer, Berlin, 1999)

  4. U. Schollwoeck, Ann. Phys. 326, 96 (2011)

    Article  ADS  MATH  Google Scholar 

  5. U. Schollwoeck, Rev. Mod. Phys. 77, 259 (2005)

    Article  ADS  Google Scholar 

  6. D.J. Rowe, Rev. Mod. Phys. 40, 153 (1968)

    Article  ADS  Google Scholar 

  7. G. Baym, L.P. Kadanoff, Phys. Rev. 124, 287 (1961)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. G. Baym, Phys. Rev. 127, 1391 (1962)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. G. Baym, Phys. Lett. 1, 242 (1962)

    Article  ADS  Google Scholar 

  10. D.S. Delion, P. Schuck, J. Dukelsky, Phys. Rev. C 72, 064305 (2005)

    Article  ADS  Google Scholar 

  11. J. Dukelsky, P. Schuck, Nucl. Phys. A 512, 466 (1990)

    Article  ADS  Google Scholar 

  12. J.G. Hirsch, A. Mariano, J. Dukelsky, P. Schuck, Ann. Phys. 296, 187 (2002)

    Article  ADS  Google Scholar 

  13. F. Catara, G. Piccitto, M. Sambataro, N. Van Giai, Phys. Rev. B 54, 17536 (1996)

    Article  ADS  Google Scholar 

  14. F. Catara, M. Grasso, G. Piccitto, M. Sambataro, Phys. Rev. B 58, 16070 (1998)

    Article  ADS  Google Scholar 

  15. A. Storozhenko, P. Schuck, J. Dukelsky, G. Röpke, A. Vdovin, Ann. Phys. 307, 308 (2003)

    Article  ADS  MATH  Google Scholar 

  16. P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1980)

  17. J. Dukelsky, G. Röpke, P. Schuck, Nucl. Phys. A 628, 17 (1998)

    Article  ADS  Google Scholar 

  18. M. Jemai, D.S. Delion, P. Schuck, Phys. Rev. C 88, 044004 (2013)

    Article  ADS  Google Scholar 

  19. J.P. Blaizot, G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, 1986)

  20. J. Goldstone, Nuovo Cimento 19, 154 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  21. W. Kohn, Phys. Rev. 123, 1242 (1961)

    Article  ADS  MATH  Google Scholar 

  22. J. Reidl, G. Bene, R. Graham, P. Szépfalusy, Phys. Rev. A 63, 043605 (2001)

    Article  ADS  Google Scholar 

  23. P.W. Anderson, Physica B 112, 1900 (1958)

    Google Scholar 

  24. N.N. Bogoliubov, Sov. Phys. J. Exp. Theor. Phys. 34, 698 (1958)

    Google Scholar 

  25. R. Combescot, M.Yu. Kagan, S. Stringari, Pys. Rev. A 74, 042717 (2006)

    ADS  Google Scholar 

  26. N. Martin, M. Urban, Phys. Rev. C 90, 065805 (2014)

    Article  ADS  Google Scholar 

  27. D.R. Bes, R.A. Broglia, Nucl. Phys. 80, 289 (1966)

    Article  Google Scholar 

  28. E. Khan, N. Sandulescu, N. Van Giai, M. Grasso, Phys. Rev. C 69, 014314 (2004)

    Article  ADS  Google Scholar 

  29. M. Tohyama, P. Schuck, Eur. Phys. J. A 32, 139 (2007)

    Article  ADS  Google Scholar 

  30. M. Tohyama, P. Schuck, Phys. Rev. C 91, 034316 (2015)

    Article  ADS  Google Scholar 

  31. M. Jemai, P. Schuck, J. Dukelsky, R. Bennaceur, Phys. Rev. B 71, 085115 (2005)

    Article  ADS  Google Scholar 

  32. M. Urban, P. Schuck, Phys. Rev. A 90, 023632 (2014)

    Article  ADS  Google Scholar 

  33. S. Schaefer, P. Schuck, Phys. Rev. B 59, 1712 (1999)

    Article  ADS  Google Scholar 

  34. J. Dukelsky, P. Schuck, Phys. Lett. B 164, 164 (1999)

    Article  Google Scholar 

  35. R.W. Richardson, Phys. Rev. 141, 949 (1966)

    Article  ADS  Google Scholar 

  36. G. Holzwarth, T. Yukawa, Nucl. Phys. A 219, 125 (1974)

    Article  ADS  Google Scholar 

  37. K. Hagino, G.F. Bertsch, Phys. Rev. C 61, 024307 (2000)

    Article  ADS  Google Scholar 

  38. M. Grasso, F. Catara, Phys. Rev. C 63, 014317 (2000)

    Article  ADS  Google Scholar 

  39. M. Saarela, in Introduction to Modern Methods of Quantum Many-Body Theories and Their Applications, edited by A. Fabrocini, S. Fantoni, E. Krotscheck, Series on Advances in Quantum Many Body Theory (World Scientific, London, 2002), Vol. 7

  40. Yan He, Hao Guo, arXiv:1411.5100 (2014)

  41. G. Feldman, T. Fulton, Ann. Phys. 152, 376 (1984)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. “Horia Hulubei” National Institute of Physics and Nuclear Engineering, 407 Atomiştilor, POB MG-6, Bucharest-Măgurele, 077125, Romania

    Doru S. Delion

  2. Academy of Romanian Scientists, 54 Splaiul Independenţei, Bucharest, 050094, Romania

    Doru S. Delion

  3. Bioterra University, 81 Gârlei str., Bucharest, 013724, Romania

    Doru S. Delion

  4. Institut de Physique Nucléaire, 91406, Orsay Cedex, France

    Peter Schuck

  5. Laboratoire de Physique et Modélisation des Milieux Condensés, CNRS and Université Joseph Fourier, 25 Avenue des Martyrs, BP166, 38042, Grenoble Cedex 9, France

    Peter Schuck

  6. Kyorin University School of Medicine, Mitaka, 181-8611, Tokyo, Japan

    Mitsuru Tohyama

Authors
  1. Doru S. Delion
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Schuck
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mitsuru Tohyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Doru S. Delion.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Delion, D., Schuck, P. & Tohyama, M. Sum-rules and Goldstone modes from extended random phase approximation theories in Fermi systems with spontaneously broken symmetries. Eur. Phys. J. B 89, 45 (2016). https://doi.org/10.1140/epjb/e2016-60763-9

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2016-60763-9

Keywords

Search

Navigation