Correlation energy in a spin-polarized two-dimensional electron liquid in the high-density limit

We have obtained an analytic expression for the ring diagram contribution to the correlation energy of a two-dimensional electron liquid as a function of the uniform fractional spin polarization. Our results can be used to improve the interpolation formulas which represent the basic ingredient for the construction of modern spin-density functionals in two dimensions.

Figure 1

Plot of the scaling factor $I_R\left(p\right)$ [defined in Eq. (13)] as a function of the fractional polarization $p$. Solid line: Exact expression (14). Dashed line: Eq. (15) as obtained from the interpolation formula proposed in Ref. 2.