PAIR EXCITATIONS AND VERTEX CORRECTIONS IN FERMI FLUIDS AND THE DYNAMIC STRUCTURE FUNCTION OF TWO-DIMENSIONAL 3He

Abstract

We use the equations-of-motion approach for time-dependent pair correlations in strongly interacting Fermiliquidsto develop a theory of the excitation spectrum and the single-particle self energy in such systems. We present here the fully equations and their approximate solutions for3He. Our theory has the following properties: It reduces to both, i) the correlated random-phase approximation (RPA) for strongly interacting fermions if the two-particle-two-hole correlations are ignored, and, ii) to the Brillouin-Wigner perturbation theory for boson quantum fluids in the appropriate limit. iii) It preserves the two firstenergy-weighted sum rules,and systematically improves upon higher ones. iv) A familiar problem of the standard RPA is that it predicts a roton energy that lies more than a factor of two higher than what is found in experiments. A popular cure for this is to introduce an effective mass in the Lindhard function. No such ad-hoc assumption is invoked in our work. We demonstrate that the inclusion of pair-excitations improves the dispersion relation significantly. Finally, a novel form of the density response function is derived that arises from vertex corrections in the proper polarization.