Volume 110, Number 6, June 2015
|Number of page(s)||5|
|Section||Atomic, Molecular and Optical Physics|
|Published online||07 July 2015|
Uniqueness of density-to-potential mapping for fermionic lattice systems
1 Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University Edinburgh, EH14 4AS, UK
2 Department of Physics, University of York - York, YO10 5DD, UK
3 Institute of Chemistry, São Paulo State University - Araraquara, Brazil
Received: 14 April 2015
Accepted: 18 June 2015
We demonstrate that, for a fermionic lattice system, the ground-state particle density uniquely determines the external potential except for the sites corresponding to nodes of the wave function, and the limiting case where the Pauli exclusion principle completely determines the occupation of all sites. Our fundamental finding completes, for this general class of systems, the one-to-one correspondence between ground states, their densities, and the external potential at the base of the Hohenberg-Kohn theorem. Moreover we demonstrate that the mapping from wave function to potential is unique not just for the ground state, but also for excited states. To illustrate our findings, we develop a practical inversion scheme to determine the external potential from a given density. Our results hold for a general class of lattice models, which includes the Hubbard model.
PACS: 31.15.ec – Hohenberg-Kohn theorem and formal mathematical properties, completeness theorems / 71.10.Fd – Lattice fermion models (Hubbard model, etc.) / 71.15.Mb – Density functional theory, local density approximation, gradient and other corrections
© EPLA, 2015
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