NESSi 2.0: The Non-Equilibrium Systems Simulation package version 2.0

Abstract

Nonequilibrium Green's functions provide a powerful framework for studying quantum many-body dynamics including the laser-induced dynamics in solids. The Non-Equilibrium Systems Simulation package (NESSi) offers an efficient platform for such simulations, ranging from perturbative approaches like nonequilibrium $GW$ to nonequilibrium dynamical mean-field theory. However, simulations based on nonequilibrium Green's functions become computationally demanding when the dynamics span a large temporal range, such as from sub-femtosecond electron dynamics to the picosecond dynamics of collective modes. Due to the memory integral in the Kadanoff-Baym equations, which serve as equations of motion for nonequilibrium Green's functions, the computational cost scales as $\mathcal{O}(N_t^3)$ with the number of timesteps $N_t$, and the memory requirement scales as $\mathcal{O}(N_t^2)$. In this work, we extend NESSi by incorporating techniques that aim to overcome this bottleneck: (i) By truncating the memory integrals in the KBE to a maximum of $N_c$ timesteps, the computational complexity is reduced to $\mathcal{O}(N_t{N}_c^2)$, and the memory requirement to $\mathcal{O}(N_c^2)$. Provided that the results converge with respect to the cutoff $N_c$, memory truncation allows to extend the simulations to significantly longer times. (ii) We introduce functionalities to describe nonequilibrium steady states, i.e. time-translationally invariant nonequilibrium states. Such states are relevant for transport settings, and they provide an approximate description of slowly evolving (prethermal) nonequilibrium states.

45 pages, 11 figures