A v0-representability issue in lattice ensemble-DFT and its signature in lattice TDDFT

Thomas Rössler, Claudio Verdozzi () and Carl-Olof Almbladh
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Thomas Rössler: Mathematical Physics and European Theoretical Spectroscopy Facility (ETSF), Lund University
Claudio Verdozzi: Mathematical Physics and European Theoretical Spectroscopy Facility (ETSF), Lund University
Carl-Olof Almbladh: Mathematical Physics and European Theoretical Spectroscopy Facility (ETSF), Lund University

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 10, 1-7

Abstract: Abstract 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.

Date: 2018
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DOI: 10.1140/epjb/e2018-90205-7

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