A Real-time Dyson Expansion Scheme: Efficient Inclusion of Dynamical Correlations in Non-equilibrium Spectral Properties

TL;DR

This paper introduces a real-time Dyson expansion scheme that efficiently incorporates dynamical correlations into non-equilibrium spectral functions, capturing complex features with computational costs comparable to mean-field methods.

Contribution

The proposed scheme enables inclusion of dynamical correlations in spectral calculations with mean-field-like scaling, improving accuracy over static mean-field approaches.

Findings

Excellent agreement with exact results on test systems

Successfully captures excitonic band replicas in spectral features

Maintains computational efficiency comparable to mean-field methods

Abstract

Time-resolved photoemission spectroscopy is the key technique to probe the real-time non-equilibrium dynamics of electronic states. Theoretical predictions of the time dependent spectral function for realistic systems is however, a challenge. Employing the Kadanoff-Baym equations to find this quantity results in a cubic scaling in the total number of time steps, quickly becoming prohibitive and often fail quantitatively and even qualitatively. In comparison, mean-field methods have more favorable numerical scaling both in the number of time steps and in the complexity associated with the cost of evolving for a single time step, however they miss key spectral properties such as emergent spectral features. Here we present a scheme that allows for the inclusion of dynamical correlations to the spectral function while maintaining the same scaling in the number of time steps as for mean-field approaches, while capturing the emergent physics. Further, the scheme can be efficiently implemented on top of equilibrium real-time many-body perturbation theory schemes and codes. We see excellent agreement with exact results for test systems. Furthermore we exemplify the method on a periodic system and demonstrate clear evidence that our proposed scheme produces complex spectral features including excitonic band replicas, features that are not observed using static mean-field approaches.