Non-collinear spin-spiral phase for the uniform electron gas within Reduced-Density-Matrix-Functional Theory

The non-collinear spin-spiral density wave of the uniform electron gas is studied in the framework of Reduced-Density-Matrix-Functional Theory. For the Hartree-Fock approximation, which can be obtained as a limiting case of Reduced-Density-Matrix-Functional Theory, Overhauser showed a long time ago that the paramagnetic state of the electron gas is unstable with respect to the formation of charge or spin density waves. Here we not only present a detailed numerical investigation of the spin-spiral density wave in the Hartree-Fock approximation but also investigate the effects of correlations on the spin-spiral density wave instability by means of a recently proposed density-matrix functional.