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The Bethe-Salpeter equation (BSE) can provide an accurate description oflow-energy optical spectra of insulating crystals - even when excitonic effectsare important. However, due to high computational costs it is only possible toinclude a few bands in the BSE Hamiltonian. As a consequence, the dielectricscreening given by the real part of the dielectric function can besignificantly underestimated by the BSE. Here we show that universally accurateoptical response functions can be obtained by combining a four-point BSE-likeequation for the irreducible polarisability with a two-point Dyson equationwhich includes the higher-lying transitions within the random phaseapproximation (RPA). The new method is referred to as BSE+. It has acomputational cost comparable to the BSE but a much faster convergence withrespect to the size of the electron-hole basis. We use the method to calculaterefractive indices and electron energy loss spectra for a test set ofsemiconductors and insulators. In all cases the BSE+ yields excellent agreementwith experimental data across a wide frequency range and outperforms both BSEand RPA.

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