The generalized Kadanoff-Baym ansatz with initial correlations

Within the nonequilibrium Green's function (NEGF) formalism, the generalized Kadanoff-Baym ansatz (GKBA) has stood out as a computationally cheap method to investigate the dynamics of interacting quantum systems driven out of equilibrium. Current implementations of the NEGF-GKBA, however, suffer from a drawback: real-time simulations require noncorrelated states as initial states. Consequently, initial correlations must be built up through an adiabatic switching of the interaction before turning on any external field, a procedure that can be numerically highly expensive. In this work, we extend the NEGF-GKBA to allow for correlated states as initial states. Our scheme makes it possible to efficiently separate the calculation of the initial state from the real-time simulation, thus paving the way for enlarging the class of systems and external drivings accessible by the already successful NEGF-GKBA. We demonstrate the accuracy of the method and its improved performance in a model donor-acceptor dyad driven out of equilibrium by an external laser pulse.

Figure 1

LUMO occupation, without external fields, for the three types of calculations described in the main text. Total number of time steps is $N_t=2\times {10}^5$ and the time step is $\mathrm{\Delta }t=0.005$. (Left) Evolution using $T_{\mathrm{ic}}=100$ up to $t=100$. Top right panel: long time behavior for $T_{\mathrm{ic}}=100$. (Bottom right) Long time behavior for $T_{\mathrm{ic}}=1000$. In the right panels, we do not show the curve corresponding to calculation (c) [${\mathcal{I}}_{\mathrm{ic}}\left(t\right)=0$, see main text] due to too large oscillations.

Figure 2

LUMO occupation (top), current between LUMO and the first acceptor site (middle), and real part of ${\rho }_{HL}$ (bottom) in the presence of the external driving in Eq. (31) for the three types of calculations described in the main text. Total number of time steps is $N_t=2\times {10}^5$ and the time step is $\mathrm{\Delta }t=0.005$. The quantities are shown in the time range (0,50) (left) and (950,1000) (right).