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

Colloquium

DOI: 10.1140/epjb/e2016-60763-9

Cite this article as:
Delion, D., Schuck, P. & Tohyama, M. Eur. Phys. J. B (2016) 89: 45. doi:10.1140/epjb/e2016-60763-9

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.

Keywords

Computational Methods 

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Doru S. Delion
    • 1
    • 2
    • 3
  • Peter Schuck
    • 4
    • 5
  • Mitsuru Tohyama
    • 6
  1. 1.“Horia Hulubei” National Institute of Physics and Nuclear EngineeringBucharest-MăgureleRomania
  2. 2.Academy of Romanian ScientistsBucharestRomania
  3. 3.Bioterra UniversityBucharestRomania
  4. 4.Institut de Physique NucléaireOrsay CedexFrance
  5. 5.Laboratoire de Physique et Modélisation des Milieux Condensés, CNRS and Université Joseph FourierGrenoble Cedex 9France
  6. 6.Kyorin University School of MedicineTokyoJapan