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  Approximations based on density-matrix embedding theory for density-functional theories

Theophilou, I., Reinhard, T., Rubio, A., & Ruggenthaler, M. (2021). Approximations based on density-matrix embedding theory for density-functional theories. Electronic Structure, 3(3): 035001. doi:10.1088/2516-1075/ac1660.

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Theophilou_2021_Electron._Struct._3_035001.pdf (Publisher version), 3MB
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https://arxiv.org/abs/2103.02027 (Preprint)
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https://dx.doi.org/10.1088/2516-1075/ac1660 (Publisher version)
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 Creators:
Theophilou, I.1, 2, Author              
Reinhard, T.1, 2, 3, Author              
Rubio, A.1, 2, 4, Author              
Ruggenthaler, M.1, 2, Author              
Affiliations:
1Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              
2Center for Free Electron Laser Science, ou_persistent22              
3Dribia Data Research S.L., ou_persistent22              
4Center for Computational Quantum Physics (CCQ), Flatiron Institute, ou_persistent22              

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Free keywords: density functional theory, density matrix embedding theory, reduced density matrix
 Abstract: Recently a novel approach to find approximate exchange–correlation functionals in density-functional theory was presented (Mordovina et al 2019 J. Chem. Theory Comput. 15 5209), which relies on approximations to the interacting wave function using density-matrix embedding theory (DMET). This approximate interacting wave function is constructed by using a projection determined by an iterative procedure that makes parts of the reduced density matrix of an auxiliary system the same as the approximate interacting density matrix. If only the diagonal of both systems are connected this leads to an approximation of the interacting-to-non-interacting mapping of the Kohn–Sham approach to density-functional theory. Yet other choices are possible and allow to connect DMET with other density-functional theories such as kinetic-energy density functional theory or reduced density-matrix functional theory. In this work we give a detailed review of the basics of the DMET procedure from a density-functional perspective and show how both approaches can be used to supplement each other. We do not present a specific realization of combining density-functional methods with DMET but rather provide common grounds to facilitate future developments that encompass both approaches. We do so explicitly for the case of a one-dimensional lattice system, as this is the simplest setting where we can apply DMET and the one that was originally presented. Among others we highlight how the mappings of density-functional theories can be used to identify uniquely defined auxiliary systems and projections in DMET and how to construct approximations for different density-functional theories using DMET inspired projections. Such alternative approximation strategies become especially important for density-functional theories that are based on non-linearly coupled observables such as kinetic-energy density-functional theory, where the Kohn–Sham fields are no longer obtainable by functional differentiation of an energy expression, or for reduced density-matrix functional theories, where a straightforward Kohn–Sham construction is not feasible.

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Language(s): eng - English
 Dates: 2021-06-152021-03-042021-07-202021-08-312021-09-03
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2103.02027
DOI: 10.1088/2516-1075/ac1660
 Degree: -

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Title: Electronic Structure
Source Genre: Journal
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Publ. Info: Bristol : IOP Publishing
Pages: - Volume / Issue: 3 (3) Sequence Number: 035001 Start / End Page: - Identifier: ISSN: 2516-1075
CoNE: https://pure.mpg.de/cone/journals/resource/2516-1075