Accelerating Nonequilibrium Green functions simulations with embedding selfenergies

Abstract

Real-time nonequilibrium Green functions (NEGF) have been very successful to simulate the dynamics of correlated many-particle systems far from equilibrium. However, NEGF simulations are computationally expensive since the effort scales cubically with the simulation duration. Recently we have introduced the G1--G2 scheme that allows for a dramatic reduction to time-linear scaling [Schlünzen, Phys. Rev. Lett. 124, 076601 (2020); Joost et al., Phys. Rev. B 101, 245101 (2020)]. Here we tackle another problem: the rapid growth of the computational effort with the system size. In many situations where the system of interest is coupled to a bath, to electric contacts or similar macroscopic systems for which a microscopic resolution of the electronic properties is not necessary, efficient simplifications are possible. This is achieved by the introduction of an embedding selfenergy -- a concept that has been successful in standard NEGF simulations. Here, we demonstrate how the embedding concept can be introduced into the G1--G2 scheme, allowing us to drastically accelerate NEGF embedding simulations. The approach is compatible with all advanced selfenergies that can be represented by the G1--G2 scheme [as described in Joost et al., Phys. Rev. B 105, 165155 (2022)] and retains the memory-less structure of the equations and their time linear scaling. As a numerical illustration we investigate the charge transfer between a Hubbard nanocluster and an additional site which is of relevance for the neutralization of ions in matter.

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Cited by in corpus (6)

• Accelerating Nonequilibrium Green functions simulations: the G1-G2 scheme and beyond
• Quantum Fluctuations Approach to the Nonequilibrium $GW$-Approximation II: Density Correlations and Dynamic Structure Factor
• Two-Time Quantum Fluctuations Approach and its Relation to the Bethe--Salpeter Equation
• Thermoelectric energy conversion in molecular junctions out of equilibrium
• Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures
• Stability bounds for the generalized Kadanoff-Baym ansatz in the Holstein dimer