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

Author

Listed:
  • Doru S. Delion

    (“Horia Hulubei” National Institute of Physics and Nuclear Engineering
    Academy of Romanian Scientists
    Bioterra University)

  • Peter Schuck

    (Institut de Physique Nucléaire
    Laboratoire de Physique et Modélisation des Milieux Condensés, CNRS and Université Joseph Fourier)

  • Mitsuru Tohyama

    (Kyorin University School of Medicine)

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.

Suggested Citation

  • Doru S. Delion & Peter Schuck & Mitsuru Tohyama, 2016. "Sum-rules and Goldstone modes from extended random phase approximation theories in Fermi systems with spontaneously broken symmetries," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(2), pages 1-12, February.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:2:d:10.1140_epjb_e2016-60763-9
    DOI: 10.1140/epjb/e2016-60763-9
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