Time-dependent Stochastic Bethe-Salpeter Approach

TL;DR

This paper introduces a stochastic, time-dependent approach to solving the Bethe-Salpeter equation for electron-hole excitations, enabling efficient analysis of large nanocrystals with improved computational scaling.

Contribution

It develops a novel stochastic time-dependent BSE method that significantly reduces computational complexity for large extended systems.

Findings

Successfully applied to silicon and CdSe nanocrystals with up to 3000 electrons.

Achieved quadratic scaling in computational effort, improving over traditional methods.

Provided accurate optical absorption spectra for large nanostructures.

Abstract

A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the connection between time-dependent Hartree-Fock (TDHF) theory and configuration-interaction with single substitution (CIS) method. This results in a time dependent Schr\"odinger-like equation for the quasiparticle orbital dynamics based on an effective Hamiltonian containing direct Hartree and screened exchange terms, where screening is described within the Random Phase Approximation (RPA). To solve for the optical absorption spectrum, we develop a stochastic formulation in which the quasiparticle orbitals are replaced by stochastic orbitals to evaluate the direct and exchange terms in the Hamiltonian as well as the RPA screening. This leads to an overall quadratic scaling, a significant improvement over the equivalent symplectic eigenvalue representation of the BSE. Application of the time-dependent stochastic BSE (TDsBSE) approach to silicon and CdSe nanocrystals up to size of ~3000 electrons is presented and discussed.