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
a e-mail: Claudio.Verdozzi@teorfys.lu.se
Received:
26
March
2018
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.
© 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.
