Eur. Phys. J. B (2016) 89: 45
https://doi.org/10.1140/epjb/e2016-60763-9

Colloquium

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

¹ “Horia Hulubei” National Institute of Physics and Nuclear Engineering, 407 Atomiştilor, POB MG-6, Bucharest-Măgurele, 077125, Romania
² Academy of Romanian Scientists, 54 Splaiul Independenţei, Bucharest, 050094, Romania
³ Bioterra University, 81 Gârlei str., Bucharest, 013724, Romania
⁴ Institut de Physique Nucléaire, 91406 Orsay Cedex, France
⁵ Laboratoire de Physique et Modélisation des Milieux Condensés, CNRS and Université Joseph Fourier, 25 Avenue des Martyrs BP166, 38042 Grenoble Cedex 9, France
⁶ Kyorin University School of Medicine, Mitaka, 181-8611 Tokyo, Japan

^a e-mail: delion@theory.nipne.ro

Received: 21 September 2015
Received in final form: 2 December 2015
Published online: 17 February 2016

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.