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  One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures

Giesbertz, K. J. H., & Ruggenthaler, M. (2019). One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures. Physics Reports: Review Section of Physics Letters, 806, 1-47. doi:10.1016/j.physrep.2019.01.010.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0001-AFE2-B Version Permalink: http://hdl.handle.net/21.11116/0000-0004-94F7-E
Genre: Journal Article

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 Creators:
Giesbertz, K. J. H1, Author
Ruggenthaler, M.2, 3, Author              
Affiliations:
1Theoretical Chemistry, Faculty of Exact Sciences, VU University, ou_persistent22              
2Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              
3Center for Free-Electron Laser Science, ou_persistent22              

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Free keywords: one-body reduced density matrix, v-representability, finite temperature, finite basis set DFT
 Abstract: In this review we provide a rigorous and self-contained presentation of one-body reduced density-matrix (1RDM) functional theory. We do so for the case of a finite basis set, where density-functional theory (DFT) implicitly becomes a 1RDM functional theory. To avoid non-uniqueness issues we consider the case of fermionic and bosonic systems at elevated temperature and variable particle number, i.e, a grand-canonical ensemble. For the fermionic case the Fock space is finite-dimensional due to the Pauli principle and we can provide a rigorous 1RDM functional theory relatively straightforwardly. For the bosonic case, where arbitrarily many particles can occupy a single state, the Fock space is infinite-dimensional and mathematical subtleties (not every Hermitian Hamiltonian is self-adjoint, expectation values can become infinite, and not every self-adjoint Hamiltonian has a Gibbs state) make it necessary to impose restrictions on the allowed Hamiltonians and external non-local potentials. For simple conditions on the interaction of the bosons a rigorous 1RDM functional theory can be established, where we exploit the fact that due to the finite one-particle space all 1RDMs are finite- dimensional. We also discuss the problems arising from 1RDM functional theory as well as DFT formulated for an infinite-dimensional one-particle space.

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Language(s): eng - English
 Dates: 2019-01-312018-04-072019-01-312019-02-122019-05-10
 Publication Status: Published in print
 Pages: 48
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: arXiv: 1710.08805
DOI: 10.1016/j.physrep.2019.01.010
 Degree: -

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Title: Physics Reports: Review Section of Physics Letters
Source Genre: Journal
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Publ. Info: Amsterdam : North-Holland
Pages: 48 Volume / Issue: 806 Sequence Number: - Start / End Page: 1 - 47 Identifier: ISSN: 0370-1573
CoNE: https://pure.mpg.de/cone/journals/resource/954925524775