Time-dependent density-functional and reduced density-matrix methods for few electrons: Exact versus adiabatic approximations

TL;DR

This paper compares exact and approximate methods for modeling electron correlations in 1D systems under time-dependent fields, highlighting limitations of adiabatic approximations and exploring the role of static correlations.

Contribution

It evaluates the performance of local density and orbital functionals in time-dependent scenarios, emphasizing the importance of non-locality and memory effects.

Findings

Adiabatic approximations cause detuning in Rabi oscillations.

Exact solutions reveal the significance of static correlations.

Time-dependent functionals need non-locality and memory to accurately describe electron dynamics.

Abstract

To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D $N$-electron problem onto an $N$-dimensional single electron problem. We analyze the performance of the recently derived 1D local density approximation as well as the exact-exchange orbital functional for those systems. We show that the interaction with an external resonant laser field shows Rabi oscillations which are detuned due to the lack of memory in adiabatic approximations. To investigate situations where static correlations play a role, we consider the time-evolution of the natural occupation numbers associated to the reduced one-body density matrix. Those studies shed light on the non-locality and time-dependence of the exchange and correlation functionals in time-dependent density and density-matrix functional theories.