Exact Maps in Density Functional Theory for Lattice Models

New Journal Of Physics 18, (2016)

Exact Maps in Density Functional Theory for Lattice Models

Tanja Dimitrov,Heiko Appel,Johanna I. Fuks, Angel Rubio

In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening. We show that for fully decoupled subsystems the intra-system steepening transforms into the well-known inter-system derivative discontinuity. An important conclusion is that for e.g. charge transfer processes between localized fragments within the same system it is not the usual inter-system derivative discontinuity that is missing in common ground-state functionals, but rather the differentiable intra-system steepening that we illustrate in the present work.

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The authors thank Professor Matthias Scheffler for his support, Johannes Flick, Jessica Walkenhorst and Viktor Atalla for very useful discussions and comments, and Nicola Kleppmann, Teresa Reinhard and Anne Hodgson for comments on the manuscript. We acknowledge financial support from the European Research Council Advanced Grant DYNamo (ERC-2010- AdG-267374), Spanish Grant (FIS2013-46159-C3-1-P), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), COST Actions CM1204 (XLIC), and MP1306 (EUSpec).

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