Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas

We present an analytical expression for the static many-body local field factor G₊(q) of a homogeneous two-dimensional electron gas, which reproduces diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number q. This allows us to also provide a closed-form expression for the exchange and correlation kernel Kxc(r), which represents a key input for density functional studies of inhomogeneous systems.