Static and Time-Dependent Density-Functional Theories for Strongly Correlated Materials

A special issue of Computation (ISSN 2079-3197). This special issue belongs to the section "Computational Chemistry".

Deadline for manuscript submissions: closed (31 August 2020) | Viewed by 4934

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Guest Editor
Department of Physics, University of Central Florida, Orlando, FL 32816, USA
Interests: computational and theoretical condensed matter physics; materials with strong electron-electron correlations; excitations in novel materials; ultrafast charge dynamics in Mott insulators and semiconductors; nanomagnetism

Special Issue Information

Dear Colleagues,

Recent developments of the static and time-dependent density functional theory (DFT and TDDFT) have led to a dramatic progress in the accurate description of the properties of various types of systems, from molecules and nanostructures and bulk materials. However, in the case of one of the most important and complicated groups of materials—systems with strong electron–electron correlations, the community is in desperate need of the ab initio tools, most notably with universal exchange-correlation (XC) potential. Strongly correlated materials are systems with partially-filled valence d- or/and f-orbital bands of electrons with rather localized charges. As a result of such a localization, in these systems the width of the corresponding bands (or kinetic energy) is often smaller or of the same order as the energy of the local on-site Coulomb repulsion between the electrons (or potential energy). The delicate interplay of the kinetic and potential energy effects results in many unusual and potentially useful properties of strongly correlated materials, like giant magneto-resistance and high-temperature superconductivity. Due to a strongly nonhomogeneous distribution of charges in these systems, LDA, GGA and other standard approaches fail to describe their properties. Thus, currently developers are exploring different alternative directions to construct the corresponding appropriate XC potentials for these systems in the static (DFT) and time-dependent (TDDFT) cases and to apply them to variety of strongly correlated systems.

We invite researchers working in the field to contribute to this Special Issue by submitting papers on their original research and reviews on the current state-of-the-art and prospects of the field.

Dr. Volodymyr Turkowski
Guest Editor

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Published Papers (2 papers)

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Research

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23 pages, 2121 KiB  
Article
Nonadiabatic Exchange-Correlation Potential for Strongly Correlated Materials in the Weak and Strong Interaction Limits
by Volodymyr Turkowski and Talat S. Rahman
Computation 2022, 10(5), 77; https://doi.org/10.3390/computation10050077 - 20 May 2022
Viewed by 1795
Abstract
In this work, nonadiabatic exchange-correlation (XC) potentials for time-dependent density-functional theory (TDDFT) for strongly correlated materials are derived in the limits of strong and weak correlations. After summarizing some essentials of the available dynamical mean-field theory (DMFT) XC potentials valid for these systems, [...] Read more.
In this work, nonadiabatic exchange-correlation (XC) potentials for time-dependent density-functional theory (TDDFT) for strongly correlated materials are derived in the limits of strong and weak correlations. After summarizing some essentials of the available dynamical mean-field theory (DMFT) XC potentials valid for these systems, we present details of the Sham–Schluter equation approach that we use to obtain, in principle, an exact XC potential from a many-body theory solution for the nonequilibrium electron self-energy. We derive the XC potentials for the one-band Hubbard model in the limits of weak and strong on-site Coulomb repulsion. To test the accuracy of the obtained potentials, we compare the TDDFT results obtained with these potentials with the corresponding nonequilibrium DMFT solution for the one-band Hubbard model and find that the agreement between the solutions is rather good. We also discuss possible directions to obtain a universal XC potential that would be appropriate for the case of intermediate interaction strengths, i.e., a nonadiabatic potential that can be used to perform TDDFT analysis of nonequilibrium phenomena, such as transport and other ultrafast properties of materials with any strength of electron correlation at any value in the applied perturbing field. Full article
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Review

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26 pages, 849 KiB  
Review
Recent Progress in Lattice Density Functional Theory
by T. S. Müller, W. Töws and G. M. Pastor
Computation 2019, 7(4), 66; https://doi.org/10.3390/computation7040066 - 20 Nov 2019
Cited by 4 | Viewed by 2772
Abstract
Recent developments in the density-functional theory of electron correlations in many-body lattice models are reviewed. The theoretical framework of lattice density-functional theory (LDFT) is briefly recalled, giving emphasis to its universality and to the central role played by the single-particle density-matrix γ . [...] Read more.
Recent developments in the density-functional theory of electron correlations in many-body lattice models are reviewed. The theoretical framework of lattice density-functional theory (LDFT) is briefly recalled, giving emphasis to its universality and to the central role played by the single-particle density-matrix γ . The Hubbard model and the Anderson single-impurity model are considered as relevant explicit problems for the applications. Real-space and reciprocal-space approximations to the fundamental interaction-energy functional W [ γ ] are introduced, in the framework of which the most important ground-state properties are derived. The predictions of LDFT are contrasted with available exact analytical results and state-of-the-art numerical calculations. Thus, the goals and limitations of the method are discussed. Full article
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