Dynamical local-field factors and effective interactions in the two-dimensional electron liquid

Abstract

We present an analytical study of the dynamical local-field factors associated with the response of a homogeneous two-dimensional interacting electron liquid as functions of momentum, frequency, and density. We derive sum rules that constrain their asymptotic forms ͑in momentum and frequency͒ for both the spinsymmetric and spin-antisymmetric cases. Parametrized expressions for the local-field factors are proposed, based on all available sum rules and on many-body perturbation theory, and these are found to be in good agreement with quantum Monte Carlo calculations. Finally, these expressions are used to evaluate the effective electron-electron interaction in a local approximation for two-dimensional systems. It is shown that both the quantitative and qualitative behaviors of the interaction are sensitive to the inclusion of dynamical correlations.

Structure of the local-field factor of the 2D electron fluid. Possible evidence for correlated scattering of electron pairs

“…The 2-D LFFs do not have the form indicated by standard perturbation theory [6]. Such calculations give LFFs with a "hump" at 2k F .…”

“…The subtraction of the C ∞ k term must be applied asymptotically and this leads to some arbitrariness in deciding on the "asymptotic" regime. Atwal et al [6] use what they call "an admittedly ad hoc" scheme in their Eq. (22).…”

“…As such, considerable effort has been devoted to determining G(k), using perturbation theory, kinetic-equation methods [1,2], etc. A partially analytic, semi-empirical approach invokes parametrized models constrained to satisfy sum rules [3] which fit ( [4,5,6]) to limited results obtained from quantum Monte-Carlo (QMC) simulations [7]. While these efforts have considerably extended the available data, it is still restricted to the fitted r s regime.…”

“…The Lindhard function χ 0 L (k) s often used for this purpose. However, another natural choice [6,16] is to use the "density-functional" noninteracting form χ(k) 0 containing the occupation numbers corresponding to the interacting density. The two choices mainly affect the large-k behaviour of the LFF [4].…”

Long-wavelength behavior of the dynamical spin-resolved local-field factor in a two-dimensional electron liquid

“…[15], based on the exact limiting results and sum rules. One of the sum rules employed in the scheme is the third moment sum rule.…”