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  Exact maps in density functional theory for lattice models

Dimitrov, T., Appel, H., Fuks, J. I., & Rubio, A. (2016). Exact maps in density functional theory for lattice models. New Journal of Physics, 18(8): 083004. doi:10.1088/1367-2630/18/8/083004.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-3FCD-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002B-1ECF-F
Genre: Journal Article

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http://arxiv.org/abs/1512.07456 (Preprint)
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 Creators:
Dimitrov, Tanja1, 2, Author              
Appel, Heiko1, 2, Author              
Fuks, Johanna I.3, Author
Rubio, Angel1, 2, Author              
Affiliations:
1Theory, Fritz Haber Institute, Max Planck Society, ou_634547              
2Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2074320              
3Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA, ou_persistent22              

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Free keywords: Physics; Chemical Physics; density functional theory; intrasystem steepening; derivative discontinuity; exact functional; density-to-potential map
 Abstract: 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 graphically illustrate the complete 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 and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.

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Language(s): eng - English
 Dates: 2015-12-232016-03-232016-07-082016-07-28
 Publication Status: Published online
 Pages: 18
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: arXiv: 1512.07456
DOI: 10.1088/1367-2630/18/8/083004
 Degree: -

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Title: New Journal of Physics
  Abbreviation : New J. Phys.
Source Genre: Journal
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Publ. Info: Bristol : IOP Publishing
Pages: - Volume / Issue: 18 (8) Sequence Number: 083004 Start / End Page: - Identifier: ISSN: 1367-2630
CoNE: https://pure.mpg.de/cone/journals/resource/954926913666