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MODERN APPLICATIONS OF COVARIANT DENSITY FUNCTIONAL THEORY∗

Peter A. Ring, H. Abusara, A. V. Afanasjev, George A. Lalazissis, D. Vretenar

Published Jan 1, 2011• 6 citations
OpenAlex

Abstract

Modern applications of Covariant Density Functional Theory (CDFT) are discussed. First we show a systematic investigation of fission barriers in actinide nuclei within constraint relativistic mean field theory allowing for triaxial deformations. In the second part we discuss a microscopic theory of quantum phase transitions (QPT) based on the relativistic generator coordinate method.

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We discuss two basic problems in the Hohenberg-Kohn-Sham version of density functional theory, HKS-DFT: the first, the N-representability of the functional F[ρ] and, the second, the universality of F[ρ]. In relation to the first, we show that F[ρ] must satisfy N-representability conditions that follow from those on the 2-matrix D2(r1, r2; r′, r′2). In the case of the second, we provide arguments based on the equivalence between ab initio DFT and HKS-DFT to show that the functional F[ρ] is not universal.

International Journal of Modern Physics B•Oct 20, 2008•12 citations
Modern applications of Covariant Density Functional Theory (CDFT) are discussed. First we show a systematic investigation of fission barriers in actinide nuclei within constraint relativistic mean field theory allowing for triaxial deformations. In the second part we discuss a microscopic theory of quantum phase transitions (QPT) based on the relativistic generator coordinate method.
Density-functional theory (DFT) is shown to provide a conceptual and computational framework for entanglement in interacting many-body quantum systems. DFT can, in particular, shed light on the intriguing relationship between quantum phase transitions and entanglement. We use DFT concepts to express entanglement measures in terms of the first or second derivative of the ground-state energy. We illustrate the versatility of the DFT approach via a variety of analytically solvable models. As a further application we discuss entanglement and quantum phase transitions in the case of mean-field approximations for realistic models of many-body systems.
Density functional theory is a rapidly developing branch of many-particle physics that has found applications in atomic, molecular, solid state and nuclear physics. This text describes the conceptual framework of density functional theory and discusses in detail the derivation of explicit functionals from first principles as well as their application to Coulomb systems. Both non-relativistic and relativistic systems are treated. The connection of density functional theory with other many-body methods is highlighted. The presentation is self-contained; the book is thus suited for a graduate course on density functional theory.
Constrained density-functional theory (CDFT) has been used by several authors for determining model Hamiltonian parameters of high- superconductors and other transition metal compounds. These methods use the fact that the orbitals are well localized and can easily be split into atomic components. We generalize them to systems with relatively delocalized electrons, so that they can be used, for example, for determining parameters for a Hubbard model of conducting polymers (e.g., polyacetylene). We selected the molecule and a linear C chain as test cases. The results of the constrained density-functional calculations were fitted to Hartree-Fock model calculations of the Hubbard model. In the case of we also fitted the CDFT results to exact solutions of the Hubbard model. For we found a substantial discrepancy between the U -values from the exact and the Hartree-Fock model calculations, which shows that it is important to specify the approximations that are used in determining the model parameters. On the other hand, the CDFT calculations themselves lead to roughly uniquely defined model parameters.
We discuss two basic problems in the Hohenberg-Kohn-Sham version of density functional theory, HKS-DFT: the first, the N-representability of the functional F[ρ] and, the second, the universality of F[ρ]. In relation to the first, we show that F[ρ] must satisfy N-representability conditions that follow from those on the 2-matrix D2(r1, r2; r′, r′2). In the case of the second, we provide arguments based on the equivalence between ab initio DFT and HKS-DFT to show that the functional F[ρ] is not universal.