Dynamical correlations in the one-dimensional electron gas with short-range interactions

Abstract:

We study the dynamical correlation effects in a one-dimensional Fermion gas with repulsive delta-function interaction within the quantum version of the self-consistent field approximation of Singwi, Tosi, Land, and Sjölander [Phys. Rev. 176, 589 (1968)]. The dynamic correlation effects are described by a frequency dependent local-field correction G(q,w). There is a corresponding local-field factor G(q,w) for the spin-density correlations. We investigate the structure factors, spin-dependent pair-correlation functions, the frequency dependences of G(q,w) and G(q,w), and the plasmon dispersion relation within this formalism. We compare our results with other theoretical approaches, in particular the static version of the self-consistent field approximation to highlight the importance of dynamical correlations.