Efficient O(N2) method to solve the Bethe-Salpeter equation -: art. no. 085307

We present a numerically efficient approach to solve the Bethe-Salpeter equation for the polarization function. Rather than from the usual eigenvalue representation, the macroscopic polarizability is obtained from the solution of an initial-value problem. This reduces the computational effort considerably and allows for calculating excitonic and local-field effects in optical spectra of complex systems consisting of many atoms. As an example we investigate the optical anisotropy of the monohydride Si(001)(2x1) surface. While excitonic effects influence the surface optical properties considerably, the local-field effect induced changes are minimal.