Influence of Markovianity and self-consistency on time-resolved spectral functions of driven quantum systems

TL;DR

This paper compares the real-time Dyson expansion with established non-equilibrium Green's function methods for simulating driven quantum systems, showing RTDE's ability to accurately capture correlation effects and spectral features.

Contribution

It introduces RTDE as an efficient method that bridges mean-field and full KBE simulations, accurately capturing dynamical correlations in driven quantum systems.

Findings

RTDE reliably reproduces density matrix trajectories across interaction strengths.

RTDE captures long-lived oscillations and revivals in Green's functions.

RTDE reveals non-equilibrium spectral features like quasiparticle splittings.

Abstract

We present a systematic comparison of the real-time Dyson expansion (RTDE) with established non-equilibrium Green's function approaches for simulating driven, interacting quantum systems. Focusing on density matrix dynamics, time-off-diagonal Green's functions, and time-resolved photoemission spectra, we benchmark RTDE against fully self-consistent Kadanoff-Baym equation (KBE) calculations, the generalized Kadanoff-Baym ansatz (GKBA), and exact diagonalization for small systems using second order many-body perturbation theory. Using a driven two-band Hubbard model, we show that mean-field single particle density matrix trajectories provide a reliable baseline for RTDE across a broad range of interaction strengths and excited-carrier populations. Further, RTDE accurately captures correlation effects in the Green's functions, including long-lived oscillations and revivals that are strongly suppressed by the overdamping inherent to self-consistent KBE schemes. As a consequence, RTDE resolves rich non-equilibrium spectral structure in time-resolved photoemission, such as interaction- and population-dependent quasiparticle splittings and bandgap renormalization, which are largely washed out in self-consistent approaches, yet are present in the exact solutions. Our results demonstrate that RTDE bridges the gap between mean-field propagation and full two-time KBE simulations, retaining favorable linear scaling while capturing essential dynamical correlations relevant for ultrafast spectroscopy.