Ground-state properties of quasi-one-dimensional electron systems within dynamic local-field correction: Quantum Singwi-Tosi-Land-Sjölander theory

Abstract

Dynamic local-field correction (LFC) brings a richer picture about the description of a many-body system than the standard mean-field theories. Here we investigate the ground-state properties of a quasi-one-dimensional electronic system using the quantum version of the Singwi-Tosi-Land-Sj\"olander (STLS) theory and present a critical account of its performance. The results are markedly different than those theories based on static LFC and the random-phase approximation; an example is the static structure factor, which develops a significant peak at low densities, signaling a developing ordered phase. An indication of growing instability at low densities is seen on $G(q,0)$, the static behavior of the dynamic LFC, which has an oscillatory character with a magnitude exceeding unity, peaking exactly at ${4k}_{F}.$ The pair-correlation function comes out as positive for the densities considered in this work. The correlation energy and the compressibility curves are seen to be quite close to the static STLS results. A flaw of the theory is the significantly negative values of the dynamic structure factor around the plasmon frequencies, also the lifetime of the plasmons turns out to be negative away from the single-pair continuum. In summary, the major shortcomings of the dynamic STLS scheme are the violation of the compressibility sum rule (as in the static STLS case) and the misrepresentation of the plasmons in the dynamic structure factor.