Exploring weightdependent densityfunctional approximations for ensembles in the Hubbard dimer
Abstract
GrossOliveiraKohn densityfunctional theory (GOKDFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground and excitedstate densities. The ensemble energy (i.e. the weighted sum of ground and excitedstate energies) can be obtained variationally as a functional of the ensemble density. Like in DFT, the key ingredient to model in GOKDFT is the exchangecorrelation functional. Developing densityfunctional approximations (DFAs) for ensembles is a complicated task as both density and weight dependencies should in principle be reproduced. In a recent paper [K. Deur et al., Phys. Rev. B 95, 035120 (2017)], the authors applied exact GOKDFT to the simple but nontrivial Hubbard dimer in order to investigate (numerically) the importance of weight dependence in the calculation of excitation energies. In this work, we derive analytical DFAs for various density and correlation regimes by means of a LegendreFenchel transform formalism. Both functional and density driven errors are evaluated for each DFA. Interestingly, when the ensemble exactexchangeonly functional is used, these errors can be large, in particular if the dimer is symmetric, but they cancel each other so that the excitation energies obtained by linear interpolation are always accurate, even in the strongly correlated regime.
 Publication:

European Physical Journal B
 Pub Date:
 July 2018
 DOI:
 10.1140/epjb/e2018901247
 arXiv:
 arXiv:1803.00291
 Bibcode:
 2018EPJB...91..162D
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Physics  Chemical Physics
 EPrint:
 18 pages, 13 figures