Spin Polarization Resolved Energetics of a Quasi One Dimensional Electron Gas

This work extends that of Casula et. al.$^1$ by using Quantum Monte Carlo to calculate the exact energy of a quasi one dimensional electron gas at nonzero polarizations. We present a parameterization of the correlation energy suitable for LSDA density functional calculations$^2$. The energy of the momentum resolved spin and charge excitations is also calculated via the intermediate scattering function$^3$. At low densities, correlation opens a gap for charge excitations near $2 k_f$ for each spin species. The modes with periodicity close to the mean interparticle spacing are softened due to the formation of a quasi Wigner crystal. These effects disappear as the density increases and correlation becomes less important. The calculated excitation spectrum agrees with the long wavelength behavior predicted by Luttinger liquid theory. \begin{itemize} \item[{[1]}] M. Casula, S. Sorella and G. Senatore, cond-mat/0607130 (2006) \item[{[2]}] Abedinpour, Polini, Xianlong and Tosi, private communication. \item[{[3]}] S. Yamamoto, Physical Review Letters, {\bf 75}, 3349 (1995) \end{itemize}