Non-equilibrium Green's function approach to inhomogeneous quantum many-body systems using the Generalized Kadanoff Baym Ansatz

TL;DR

This paper discusses an extension of the Generalized Kadanoff-Baym Ansatz (GKBA) to inhomogeneous quantum many-body systems, enabling efficient non-equilibrium Green's function calculations for complex, strongly correlated systems.

Contribution

The paper extends the GKBA method to inhomogeneous, strongly correlated quantum systems, providing a practical approach for long-time non-equilibrium simulations.

Findings

Successful application to a 2-electron quantum well

Accurate description of correlated electron dynamics

Reduced computational complexity for time-dependent calculations

Abstract

In non-equilibrium Green's function calculations the use of the Generalized Kadanoff-Baym Ansatz (GKBA) allows for a simple approximate reconstruction of the two-time Green's function from its time-diagonal value. With this a drastic reduction of the computational needs is achieved in time-dependent calculations, making longer time propagation possible and more complex systems accessible. This paper gives credit to the GKBA that was introduced 25 years ago. After a detailed derivation of the GKBA, we recall its application to homogeneous systems and show how to extend it to strongly correlated, inhomogeneous systems. As a proof of concept, we present results for a 2-electron quantum well, where the correct treatment of the correlated electron dynamics is crucial for the correct description of the equilibrium and dynamic properties.