Linear response time-dependent density functional theory of the Hubbard dimer

Diego J. Carrascal, Jaime Ferrer (), Neepa Maitra and Kieron Burke
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Diego J. Carrascal: Universidad de Oviedo
Jaime Ferrer: Universidad de Oviedo
Neepa Maitra: Hunter College, City University of New York
Kieron Burke: University of California

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 7, 1-21

Abstract: Abstract The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequency-dependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequency-dependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the ground-state exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. Many exact results, limits, and expansions about those limits are given in the Appendices.

Date: 2018
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DOI: 10.1140/epjb/e2018-90114-9

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