EPJB Colloquium - Fulfillment of sum-rules and Goldstone modes in many body theories
- Published on 15 February 2016
This EPJ B Colloquium article explores applications of the Self-Consistent Random Phase Approximation (SCRPA) approach to Fermi systems with a continuously broken symmetry. Correlations beyond those considered by standard Random Phase Approximation (RPA) are summed up, thereby correcting for the quasi-boson approximation in standard RPA.
Desirable properties of standard RPA, such as fulfilment of the energy-weighted sum rule and the appearance of Goldstone (zero) modes, are preserved. The authors show theoretically as well as numerically, for a model case, that SCRPA maintains all the properties of standard RPA for practically all instances of spontaneously-broken symmetries. A simpler approximate form of SCRPA, the so-called renormalised RPA, also exhibits these properties. The SCRPA equations are first outlined as an eigenvalue problem, and then it is shown how an equivalent many-body Green’s function approach can be formulated.
Doru S. Delion, Peter Schuck, and Mitsuru Tohyama (2016),
Sum-rules and Goldstone modes from extended random phase approximation theories in Fermi systems with spontaneously broken symmetries,
European Physical Journal B, DOI: 10.1140/epjb/e2016-60763-9