Dynamic correlation effects on correlational properties of finite-temperature quasi-one-dimensional electron gas

We have studied correlational properties of quasi-one-dimensional electron gas at finite temperatureTby incorporating the dynamics of electron correlations within the quantum version of the self-consistent mean-field approach of Singwi, Tosi, Land, and Sjölander. Static structure factor, pair-correlation function, static density susceptibility, excess kinetic energy, and free correlation energy are calculated covering a wide range of temperature and electron number density. As at absolute zero temperature, the inclusion of dynamics of correlations results in stronger spatial electron correlations, with a pronounced peak in the static structure factor at wave vectorq∼ 3.5k_F, which grows further with decreasing electron density. Below a critical density, the static density susceptibility seems to diverge at this value ofq, signaling a transition from liquid to the Wigner crystal state-a prediction in qualitative agreement with recent simulations and experiment. However, thermal effects tend to impede crystallization with the consequence that the critical density decreases significantly with risingT. On the other hand, the pair-correlation function at short range exhibits a non-monotonic dependence onT, initially becoming somewhat stronger with risingTand then weakening continuously above a sufficiently highT. The calculated free correlation energy shows a noticeable dependence onT, with its magnitude increasing with increase inT. Further, we have looked into the effect of temperature on the frequency-dependence of dynamic local-field correction factor and the plasmon dispersion. It is found that with risingTthe dynamics of correlations weakens, and the plasmon frequency exhibits a blue shift. Wherever interesting, we have compared our results with the lower-order approximate calculations and zero-Tquantum Monte Carlo simulations.