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

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.

7 pages, 7 Figures. Accepted for publication in Physical Review B

References in corpus (4)

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• The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect
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Cited by in corpus (7)

• The Hubbard Dimer: A density functional case study of a many-body problem
• Inverse Kohn-Sham Density Functional Theory: Progress and Challenges
• Time-resolved spectroscopy in time dependent density functional theory: An exact condition
• Non-Adiabatic Approximations in Time-Dependent Density Functional Theory: Progress and Prospects
• Linear response time-dependent density functional theory of the Hubbard dimer
• Exploring non-adiabatic approximations to the exchange-correlation functional of TDDFT
• The Exact Exchange-Correlation Potential in Time-Dependent Density Functional Theory: Choreographing Electrons with Steps and Peaks