https://doi.org/10.1140/epjb/e2018-90205-7
Regular Article
A v0-representability issue in lattice ensemble-DFT and its signature in lattice TDDFT★
Mathematical Physics and European Theoretical Spectroscopy Facility (ETSF), Lund University,
22100
Lund, Sweden
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Received:
26
March
2018
Received in final form:
2
July
2018
Published online: 1
October
2018
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.
Contribution to the Topical Issue “Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.
© The Author(s) 2018. This article is published with open access at Springerlink.com
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
