Finite-T correlations and free exchange-correlation energy of quasi-one-dimensional electron gas

We have studied the effect of temperature on static density density correlations and plasmon excitation spectrum of quasi-one-dimensional electron gas (Q1DEG) using the random phase approximation (RPA). Numerical results for static structure factor, pair-correlation function, static density susceptibility, free exchange-correlation energy and plasmon dispersion are presented over a wide range of temperature and electron density. As an interesting result, we find that the short-range correlations exhibit a non-monotonic dependence on temperature T, initially growing stronger (i.e. the pair correlation function at small inter-electron spacing assuming relatively smaller values) with increasing T and then weakening above a critical T. The cross-over temperature is found to increase with increasing coupling among electrons. Also, the q = 2 k(F) peak in the static density susceptibility chi(q, omega = 0, T) at T = 0 K smears out with rising T. The free exchange-correlation energy and plasmon dispersion show a significant variation with T, and the trend is qualitatively the same as in higher dimensions.