Time-linear scaling nonequilibrium Green's function method for real-time simulations of interacting electrons and bosons. II. Dynamics of polarons and doublons
Y. Pavlyukh, Enrico Perfetto, Daniel Karlsson, Robert van Leeuwen, Gianluca Stefanucci
Abstract
Nonequilibrium dynamics of the open chain Holstein-Hubbard model is studied using the linear time-scaling $\mathrm{GKBA}+\mathrm{ODE}$ 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 ($e\text{\ensuremath{-}}e$) 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.