Real-Time Approach to the Dynamical Bethe-Salpeter Equation for Finite Systems

Abstract

We present a real-time linear-response approach to solving the dynamical Bethe-Salpeter equation (BSE). The polarization part of the screened interaction is obtained from time-dependent Hartree propagation of the one-particle density matrix within an orbital basis-set representation. The frequency convolution defining the dynamical kernel is evaluated as a product in time, avoiding numerical integration and storage of the full screened Coulomb operator. The resulting nonlinear eigenvalue problem is then solved directly, going beyond the static screening approximation with full-frequency dependence in the screened interaction. While the deterministic scaling remains $\mathcal{O}(N^6)$, the time propagation formulation is readily compatible with grid-based stochastic sampling methods, which will open the possibility for dynamical BSE calculations of very large systems.