A v0-representability issue in lattice ensemble-DFT and its signature in lattice TDDFT★
Mathematical Physics and European Theoretical Spectroscopy Facility (ETSF), Lund University,
a e-mail: Claudio.Verdozzi@teorfys.lu.se
Received in final form: 2 July 2018
Published online: 1 October 2018
We study a small Anderson-impurity cluster using lattice density functional methods, and try to determine the exact exchange-correlation (XC) potential via reverse engineering. In doing so we find singlet–triplet degenerate interacting ground states which cannot be v0-represented in an ensemble-DFT sense. We also find that it is possible to represent a triplet ground state as a pure state, but not the singlet. We further investigate this behavior within time-dependent density-functional theory. Starting from a v0-representable ground state and entering the degeneracy region via a time-dependent perturbation, we determine via reverse-engineering the time-dependent XC potential for progressively slower perturbations. This analysis shows that, even in a constant external field, the XC potential must retain a time-oscillating pattern to ensure a density constant in time, a hint of the underlying representability issue in the ground state.
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