English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Exact maps in density functional theory for lattice models

MPS-Authors
/persons/resource/persons49296

Dimitrov,  Tanja
Theory, Fritz Haber Institute, Max Planck Society;
Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

/persons/resource/persons21304

Appel,  Heiko
Theory, Fritz Haber Institute, Max Planck Society;
Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

/persons/resource/persons22028

Rubio,  Angel
Theory, Fritz Haber Institute, Max Planck Society;
Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

External Resource
Fulltext (public)

1512.07456.pdf
(Preprint), 2MB

njp_18_8_083004.pdf
(Publisher version), 6MB

Supplementary Material (public)
There is no public supplementary material available
Citation

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.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-3FCD-9
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.