Memory truncated Kadanoff-Baym equations

The Keldysh formalism for nonequilibrium Green's functions is a powerful theoretical framework the description of electronic structure, spectroscopy, and dynamics strongly correlated systems. However, underlying Kadanoff-Baym equations (KBE) two-time involve memory kernel which results in high computational cost long simulation times $t_\text{max}$, with cubic scaling computation time $t_\text{max}$. Truncation can reduce to linear but required will depend on model diagrammatic approximation self-energy. We explain how truncation be incorporated into time-propagation algorithm solve KBE, investigate systematic Hubbard different parameter regimes, approximations. easier control within dynamical mean-field solutions, where it applied momentum-independent Here, up two orders magnitude longer are accessible both weak strong coupling regime, allowing study long-time phenomena such as crossover between pre-thermalization thermalization dynamics.