Accelerating nonequilibrium Green function simulations with embedding self-energies

Real-time nonequilibrium Green functions (NEGFs) have been very successfully used 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 introduced the G1-G2 scheme that allows for a dramatic reduction to time-linear scaling [N. Schlunzen et al., Phys. Rev. Lett. 124, 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 to 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 self-energy-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 self-energies that can be represented by the G1-G2 scheme [as described in J.-P. Joost et al., Phys. Rev. B 105, 165155 (2022)] and retains the memoryless 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.

Automated summary

Real-time nonequilibrium Green functions (NEGFs) have been successfully used to simulate the dynamics of correlated many-particle systems far from equilibrium. However, NEGF simulations are computationally expensive due to cubic scaling with the simulation duration. A new G1-G2 scheme has been introduced to achieve time-linear scaling and accelerate NEGF embedding simulations, allowing for efficient simplifications when a microscopic resolution of electronic properties is not necessary. Numerical illustrations of charge transfer between a Hubbard nanocluster and an additional site are presented.