Linear response time-dependent density functional theory of the Hubbard dimer
Published 2018-02-27Version 1
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. 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. Oscillator strengths are defined appropriately for lattice Hamiltonians. The exact fluctuation-dissipation formula for the ground-state exchange-correlation energy for the dimer is written down.