Accurate Dielectric Response of Solids: Combining the Bethe-Salpeter Equation with the Random Phase Approximation

The Bethe-Salpeter equation (BSE) can provide an accurate description of low-energy optical spectra of insulating crystals - even when excitonic effects are important. However, due to high computational costs it is only possible to include a few bands in the BSE Hamiltonian. As a consequence, the dielectric screening given by the real part of the dielectric function can be significantly underestimated by the BSE. Here we show that universally accurate optical response functions can be obtained by combining a four-point BSE-like equation for the irreducible polarisability with a two-point Dyson equation which includes the higher-lying transitions within the random phase approximation (RPA). The new method is referred to as BSE+. It has a computational cost comparable to the BSE but a much faster convergence with respect to the size of the electron-hole basis. We use the method to calculate refractive indices and electron energy loss spectra for a test set of semiconductors and insulators. In all cases the BSE+ yields excellent agreement with experimental data across a wide frequency range and outperforms both BSE and RPA.