Dynamic Mode Decomposition for Extrapolating Non-equilibrium Green's Functions Dynamics

TL;DR

This paper demonstrates that combining dynamical mode decomposition with the HF-GKBA method enables efficient long-time Green's function simulations in large quantum systems, maintaining high accuracy with limited data.

Contribution

It introduces a novel approach integrating DMD with HF-GKBA to reconstruct long-time NEGF dynamics, reducing computational costs in large systems.

Findings

HF-GKBA agrees well with exact results for realistic long-range interactions.

DMD can reconstruct long-time trajectories from limited initial data.

The combined method is effective for large-scale, long-time simulations.

Abstract

The HF-GKBA offers an approximate numerical procedure for propagating the two-time non-equilibrium Green's function(NEGF). Here we compare the HF-GKBA to exact results for a variety of systems with long and short-range interactions, different two-body interaction strengths and various non-equilibrium preparations. We find excellent agreement between the HF-GKBA and exact time evolution in models when more realistic long-range exponentially decaying interactions are considered. This agreement persists for long times and for intermediate to strong interaction strengths. In large systems, HF-GKBA becomes prohibitively expensive for long-time evolutions. For this reason, look at the use of dynamical mode decomposition(DMD) to reconstruct long-time NEGF trajectories from a sample of the initial trajectory. Using no more than 16\% of the total time evolution we reconstruct the total trajectory with high fidelity. Our results show the potential for DMD to be used in conjunction with HF-GKBA to calculate long time trajectories in large-scale systems.