Some open questions in TDDFT: Clues from Lattice Models and Kadanoff-Baym Dynamics

TL;DR

This paper investigates the limitations of TDDFT's linear response and adiabatic approximations using lattice models, highlighting the importance of memory effects for accurate dynamics under fast perturbations.

Contribution

It provides a detailed analysis of TDDFT on lattice models, reviews the Kadanoff-Baym equations, and proposes a method to improve the linear response scheme.

Findings

Adiabatic potentials work well for slow perturbations.

Memory effects are essential for accurate dynamics with fast external fields.

Identified drawbacks in the linearized Sham-Schlüter equation.

Abstract

Two aspects of TDDFT, the linear response approach and the adiabatic local density approximation, are examined from the perspective of lattice models. To this end, we review the DFT formulations on the lattice and give a concise presentation of the time-dependent Kadanoff-Baym equations, used to asses the limitations of the adiabatic approximation in TDDFT. We present results for the density response function of the 3D homogeneous Hubbard model, and point out a drawback of the linear response scheme based on the linearized Sham-Schl\"uter equation. We then suggest a prescription on how to amend it. Finally, we analyze the time evolution of the density in a small cubic cluster, and compare exact, adiabatic-TDDFT and Kadanoff-Baym-Equations densities. Our results show that non-perturbative (in the interaction) adiabatic potentials can perform quite well for slow perturbations but that, for faster external fields, memory effects, as already present in simple many-body approximations, are clearly required.