Spin correlations and spin-density wave phase in a finite-temperature quasi-one-dimensional electron gas

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 Singwiet alNumerical 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 temperatureTand electron couplingr. We find that the recently reported (2020J. Phys.: Condens. Matter.32335403) non-monotonicT-dependence of the contact pair-correlation functiong(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 couplingr, 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_Fabove a critical coupling for a sufficiently highT, while to a long-wavelength SDW phase at a lowT. 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-TQ1DEG. Further, if one starts with partially spin-polarized electrons, the SDW instability is found to shift to somewhat higherτandr. 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-TQ1DEG. Wherever interesting, we have compared our results with the predictions of the static version of the mean-field approach.