Time-linear scaling nonequilibrium Green's function method for real-time simulations of interacting electrons and bosons. II. Dynamics of polarons and doublons

Nonequilibrium dynamics of the open chain Holstein-Hubbard model is studied using the linear time-scaling GKBA+ODE scheme developed in Pavlyukh et al. [Phys. Rev. B 105, 125134 (2022)]. We focus on the set of parameters relevant for photovoltaic materials, i.e., a pair of electrons interacting with phonons at the crossover between the adiabatic and antiadiabatic regimes and at moderately large electron-electron interaction. By comparing with exact solutions for two corner cases, we demonstrate the accuracy of the T matrix (in the $pp$ channel) and the second-order Fan ($GD$) approximations for the treatment of electronic (e-e) and electron-phonon (e-ph) correlations, respectively. The feedback of electrons on phonons is consistently included and is shown to be mandatory for the total energy conservation. When two interactions are simultaneously present, our simulations offer a glimpse into the dynamics of doublons and polarons unveiling the formation, propagation and decay of these quasiparticles, energy redistribution between them and self-trapping of electrons.