Density Functional Theory through Legendre Transformation

Fukuda, R.; Kotani, Takao; Suzuki, Yoko; Yokojima, Satoshi

doi:10.1143/ptp.92.833

Cited by 37 publications

(96 citation statements)

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“…For simplicity, normalization factors are considered to be implicit in the functional integration measure [38,39]. The fermion density in the presence of the sources is…”

Section: A Effective Action and The Inversion Methodsmentioning

confidence: 99%

The kinetic energy density in Kohn–Sham density functional theory

Bhattacharyya¹,

Furnstahl²

2005

Nuclear Physics A

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This work continues a program to systematically generalize the Skyrme Hartree-Fock method for medium and heavy nuclei by applying effective field theory (EFT) methods to Kohn-Sham density functional theory (DFT). When conventional Kohn-Sham DFT for Coulomb systems is extended beyond the local density approximation, the kinetic energy density τ is sometimes included in energy functionals in addition to the fermion density. However, a local (semi-classical) expansion of τ is used to write the energy as a functional of the density alone, in contrast to the Skyrme approach. The difference is manifested in different single-particle equations, which in the Skyrme case include a spatially varying effective mass. Here we show how to generalize the EFT framework for DFT derived previously to reconcile these approaches. A dilute gas of fermions with short-range interactions confined by an external potential serves as a model system for comparisons and for testing power-counting estimates of new contributions to the energy functional.

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“…For simplicity, normalization factors are considered to be implicit in the functional integration measure [38,39]. The fermion density in the presence of the sources is…”

Section: A Effective Action and The Inversion Methodsmentioning

confidence: 99%

The kinetic energy density in Kohn–Sham density functional theory

Bhattacharyya¹,

Furnstahl²

2005

Nuclear Physics A

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“…This means that the computational cost for DFT is far less than for wave function methods and the calculations can be applied to heavy nuclei. DFT is naturally formulated in an effective action framework [85] and carried out using an inversion method implemented with EFT power counting [86,87,88]. The simple prototype EFT from Section 2 for a dilute system can be revisited in DFT by putting the fermions in a trap potential v ext (x) (e.g., a harmonic oscillator) and adding sources coupled to external densities [89].…”

Section: Density Functional Theory As An Eftmentioning

confidence: 99%

Effective Field Theory and Finite-Density Systems

Furnstahl

Rupak

Schäfer

2008

Annu. Rev. Nucl. Part. Sci.

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“…This section borrows from the work of Fukuda et al [57,46] and of Valiev and Fernando [58]. For a recent pedagogical review emphasizing this point of view, see [59].…”

Section: Density Functional Theorymentioning

confidence: 97%

“…Though exact in principle, it requires in practice that the exact functional is approximated in some manner. This method has a wide range of applicability in statistical mechanics, manybody physics and field-theory [46]. The discussion will be (hopefully) pedagogical, and for this reason I will begin with the example of a classical magnet.…”

Section: Functionals Local Observables and Interacting Systemsmentioning

confidence: 99%

Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure

Georges¹

2004

AIP Conference Proceedings

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Abstract. These are introductory lectures to some aspects of the physics of strongly correlated electron systems. I first explain the main reasons for strong correlations in several classes of materials. The basic principles of dynamical mean-field theory (DMFT) are then briefly reviewed. I emphasize the formal analogies with classical mean-field theory and density functional theory, through the construction of free-energy functionals of a local observable. I review the application of DMFT to the Mott transition, and compare to recent spectroscopy and transport experiments. The key role of the quasiparticle coherence scale, and of transfers of spectral weight between low-and intermediate or high energies is emphasized. Above this scale, correlated metals enter an incoherent regime with unusual transport properties. The recent combinations of DMFT with electronic structure methods are also discussed, and illustrated by some applications to transition metal oxides and f-electron materials.

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Density Functional Theory through Legendre Transformation

Cited by 37 publications

References 0 publications

The kinetic energy density in Kohn–Sham density functional theory

The kinetic energy density in Kohn–Sham density functional theory

Effective Field Theory and Finite-Density Systems

Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure

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