The generalized Kadanoff-Baym ansatz with initial correlations

Abstract

Within the non-equilibrium 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. arXiv:1806.05639v1 [cond-mat.str-el]

Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations

“…In Eq. (8) this gives rise to an additional homogeneous solution that leads to an additional collision integral in the time-diagonal KBE (2), in agreement with recent results [20,21].…”

“…This behavior can be relieved by applying the Generalized Kadanoff-Baym ansatz (GKBA) [16,17] which reduces the dynamics of the NEGF, G(t, t ), to propagation along the time diagonal, t = t . It could be demonstrated that, indeed, the expected improvement of the scaling, N 3 t → N 2 t (in the following we will use the number of discretization time steps N t = T /∆t), can be achieved in practice for the selfenergy in second order Born approximation (SOA) [18,19] where initial correlation effects can be treated even more efficiently [20,21]. It could further be shown that this approximation, in many cases, does not lead to a loss of accuracy [10,15,22].…”

Efficient computation of the second-Born self-energy using tensor-contraction operations

“…In addition, many other similar multi-index operations, such as evaluating the initial correlations collision integral in Ref. [53], might become computationally more accessible by using the tensorcontraction representations. The presented simulations in selected molecular systems provided concrete evidence of the accuracy and applicability of the tensor-contraction operations.…”

“…The correlated initial state therefore needs to be prepared by starting with an uncorrelated (or HF) system and slowly switching on the interaction (adiabatic switching procedure) [25,36,48,51]. However, the inclusion of the initial correlations has been shown to be possible also within GKBA [52][53][54].…”

Study of the energy variation in many-body open quantum systems: Role of interactions in the weak and strong coupling regimes

“…The knowledge of G gives access to all single-particle quantities (e.g., density, momentum distribution, density of states). For an interacting system the SPGF can be found by solving either the Kadanoff-Baym equations [18,29,31,32], the Dyson equation [33,34], or other equivalent techniques [35][36][37][38][39]. A crucial point is the choice of a selfenergy, which is typically a functional of the SPGF itself.…”