Beyond the Generalized Kadanoff–Baym Ansatz

Abstract

The study of electron transport is easier if the Kadanoff-Baym equations (KBE) are simplified using the Generalized Kadanoff-Baym Ansatz (GKBA). For molecular bridges, GKBA is empirically known to safely work for weak and flat tunneling functions. It fails, if either of the conditions is not satisfied. The case in point is a molecular bridge formed by an Anderson type local center treated in the mean field and linked by tunneling junctions to two ferromagnetic electrodes whose tunneling functions simulate nickel with complex sd structure. Transient magnetic currents under a constant galvanic bias between electrodes are invoked by sudden switching on of both junctions. We consider three tasks: To establish quantitative criteria for the validity of the Ansatz; to develop a practically tractable correction to the Ansatz working beyond its validity range; to obtain Generalized Master Equations (GMEs) for the one-electron distribution following from both GKBA and its corrected form avoiding thus KBE. All three points are resolved by treating first the stationary (non-equilibrium) limit and transferring the results to finite times. The corrections to the Ansatz are obtained as a stationary approximation to the vertex part of the exact reconstruction equations whose free term is the standard GKBA.

Löwdin's symmetry dilemma within Green functions theory for the one‐dimensional Hubbard model

“…For this reason, Hubbard-like models have been applied in many contexts and to a wide typology of systems, both in and out of equilibrium, see, e.g., Refs. [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations

“…However, these NEGF simulations are hampered by an unfavorable scaling with the simulation duration according to T 3 resulting from the two-time structure of the NEGF and the memory effects in the collision integral (see below). 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].…”

A many-body approach to transport in quantum systems: From the transient regime to the stationary state

“…Extensions to the single-level quantum devices have included the spin degree of freedom for the study of spin currents, magnetism and torque [57,[398][399][400][401][402][403], establishing that, e.g., tunneling magnetoresistance may transiently develop negative values, and the electronic interactions may enhance this effect. In this regard, the GKBA reconstruction has been shown to capture the essential features of magnetic tunnel currents [404][405][406][407].…”