Spin-resolved correlations at arbitrary spin polarization and ground state of a quasi-one-dimensional electron gas

We study the spin-resolved correlations at arbitrary spin polarization ζ and the ground state of a quasi-one-dimensional electron gas by using the dynamical self-consistent mean-field theory of Singwi et al. Numerical results are presented for the spin-resolved pair-correlation functions, correlation energies, and ground-state energy at selected ζ and a range of electron density rs. Our results agree nicely with the recent lattice regularized diffusion Monte Carlo simulation data at small rs and ζ. With increasing rs and/or ζ, the spin-resolved correlations become less satisfactory, but the spin-summed quantities show a reasonable agreement, thus implying a cancellation among discrepancies in the components. Interestingly, theory predicts that the like-spin correlation energy becomes little positive for rs>1.5. A comparison between the ground-state energies of the unpolarized and fully polarized spin phases reveals that the exchange–correlations may induce a phase transition to the latter above a critical rs, rsc. Importantly, the transition is in agreement with recent experiments on low density electron quantum wires. However, the stability of partially spin-polarized states could not be ascertained due to difficulty in obtaining the self-consistent density response function beyond a certain rs, preceding rsc. Using the static mean-field theory, we find that the spin-polarization transition is abrupt (i.e., the partially spin-polarized states are energetically unstable) and it occurs at nearly the same rs as in the dynamical approach.