We have studied correlational properties of quasi-one-dimensional electron gas at finite temperature T by 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 vector q ∼ 3.5k F , which grows further with decreasing electron density. Below a critical density, the static density susceptibility seems to diverge at this value of q, 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 rising T. On the other hand, the pair-correlation function at short range exhibits a non-monotonic dependence on T, initially becoming somewhat stronger with rising T and then weakening continuously above a sufficiently high T. The calculated free correlation energy shows a noticeable dependence on T, with its magnitude increasing with increase in T. 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 rising T the 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-T quantum Monte Carlo simulations.

The exchange-correlation effects in a finite-temperature quasione-dimensional electron gas, using the self-consistent mean-field theory of Singwi, Tosi, Land, and Sjölander have been theoretically investigated. The influence of temperature T is elucidated by calculating different static properties (viz. static structure factor, pair-correlation function, static density susceptibility, and free exchange-correlation energy) and the plasmon excitation spectra over a wide range of T and electron number density. Noticeable dependence on T is found, with an interesting interplay between short-range electron correlations and T. More precisely, the pair-correlation function at small separation and for a given density first becomes stronger (i.e., its value decreases) with increasing T and then weakens monotonically above a critical T, whose value increases with reduction in density. On the other hand, the plasmon energy shows a consistent blue shift with rising T. However, the critical wave vector at which plasmons enter the single electron-hole pair continuum, decreases with T. For highlighting the correction due to shortrange correlations, the results have been compared with the predictions of random-phase approximation (RPA). As for the zero-T case, the RPA is found to be reliable only in the high density domain.

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In this paper, we theoretically investigate the effect of temperature on spin correlations in an unpolarized quasi-one-dimensional electron gas (Q1DEG). The correlations are treated dynamically within quantum version of the self-consistent mean-field approach of Singwi et al Numerical results for the ↑↑ and ↑↓ components of static structure factor and pair-correlation function, and the wave vector dependent static spin and charge susceptibilities are presented over a wide range of temperature T and electron coupling r s . We find that the recently reported (2020 J. Phys.: Condens. Matter. 32 335403) non-monotonic T-dependence of the contact pair-correlation function g(r = 0; T) is driven primarily by an interplay between ↑↓ correlations and thermal effects. At a given temperature, the dynamics of both ↑↑ and ↑↓ correlations is found to become significant with increasing coupling r s , manifesting unambiguously as pronounced peak at 3.5k F (periodic oscillations) in the corresponding components of the structure factor (pair-correlation function). Analysis of static spin and charge susceptibilities reveals that an imbalance between ↑↑ and ↑↓ correlations may induce a transition to a spin-density wave (SDW) phase of wave vector ∼3.5k F above a critical coupling for a sufficiently high T, while to a long-wavelength SDW phase at a low T. Higher the temperature, higher is the predicted critical coupling for the SDW phase. Interestingly, transition to the SDW phase is found to precede the recently predicted Wigner crystal instability in the finite-T Q1DEG. Further, if one starts with partially spin-polarized electrons, the SDW instability is found to shift to somewhat higher τ and r s . In addition, we have presented results for the free exchange-correlation energy, free correlation energy, and excess kinetic energy for the unpolarized and fully spin-polarized phases of the finite-T Q1DEG. Wherever interesting, we have compared our results with the predictions of the static version of the mean-field approach.

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