Adiabatic and local approximations for the Kohn-Sham potential in time-dependent Hubbard chains

TL;DR

This paper derives exact Kohn-Sham potentials for 1D Hubbard chains under time-dependent fields, compares various approximations, and analyzes the roles of ground and excited state correlations using pair correlation functions.

Contribution

It provides exact Kohn-Sham potentials for 1D Hubbard chains and evaluates the effectiveness of adiabatic and local approximations in time-dependent DFT.

Findings

The exact $V_{KS}$ can be obtained from many-body dynamics.

Local approximations are insufficient for accurate $V_{xc}$.

The IGS approximation can outperform the adiabatic approach in some cases.

Abstract

We obtain the exact Kohn-Sham potentials $V_{\mathrm{KS}}$ of time-dependent density-functional theory for 1D Hubbard chains, driven by a d.c.\ external field, using the time-dependent electron density and current density obtained from exact many-body time-evolution. The exact $V_{\mathrm{xc}}$ is compared to the adiabatically-exact $V_{\mathrm{xc}}^{\mathrm{ad}}$ and the "instantaneous ground state" $V_{\mathrm{xc}}^{\mathrm{igs}}$. The latter is shown to work effectively in some cases when the former fails. Approximations for the exchange-correlation potential $V_{\mathrm{xc}}$ and its gradient, based on the local density and on the local current density, are also considered and both physical quantities are observed to be far outside the reach of any possible local approximation. Insight into the respective roles of ground-state and excited-state correlation in the time-dependent system, as reflected in the potentials, is provided by the pair correlation function.