Real-Time Exciton Dynamics with Exciton-phonon coupling via a Lindbladian Density-Matrix Framework from first-principles

We develop a real-time Lindblandian dynamics framework to study exciton dynamics with exciton–phonon coupling from first-principles. Starting from solving the Bethe–Salpeter equation (BSE), we construct an effective excitonic Hamiltonian that includes exciton–phonon interactions responsible for phonon-assisted scattering between excitonic states. The Lindblad formalism describes relaxation and dephasing processes arising from coupling to the lattice environment. Building upon the exciton–phonon Lindblad formalism of Guo et al. [1], where exciton occupations were treated within a semiclassical (diagonal) approximation, we propagate the full exciton density matrix which includes populations and coherence . This captures phonon-mediated relaxation and decoherence of excitons on equal footing, providing a full quantum treatment of exciton–phonon coupling with inputs of first-principles matrix elements from finite-momentum BSE calculations. We apply the method to prototypical systems, for example bulk hexagonal boron nitride (hBN), establishing a basis for studying exciton dynamics and decoherence, as well as other quantum mechanical observables based on two-particle density-matrices within a unified, first-principles framework.

[1] C. Guo, G. Riva, J. Simoni, J. Xu, and Y. Ping, Phys. Rev. B 112, L161111 (2025).