International Conference on Strongly Correlated Electron Systems (SCES)

A Calculation Scheme for the Pair-Density Functional Theory for the Superconductor

Katsuhiko Higuchi, Masahiko Higuchi

Published Mar 18, 2020• 1 citation

Abstract

The pair-density functional theory for the superconductor (SC-PDFT) is one of first-principles theories for the superconductor.The feature of the SC-PDFT is that the fluctuation of the particle number of the superconducting state can be reproduced via the pair-density (PD) and electron density (ED).In this paper, we present a calculation scheme for the SC-PDFT.Specifically, in order to construct a calculation scheme, the searching region for PDs and EDs is devised with a reference to results of the uniform system, and the entropy functional is developed in a functional form in terms of the PD and ED.

DOI: 10.7566/jpscp.30.011006

Related papers

Basic Variables to Be Reproduced in the First-Principles Theory for Superconductors: Fluctuation of the Particle Number

Katsuhiko Higuchi, Eina Miki, Masahiko Higuchi

arXiv:1512.07775Journal of the Physical Society of JapanMay 11, 20179 citations

Pair density-functional theory by means of the correlated wave function

Masahiko Higuchi, Katsuhiko Higuchi

arXiv:cond-mat/0610725Physical Review AApr 19, 200734 citations

A pair density functional theory utilizing the correlated wave function

Masahiko Higuchi, Katsuhiko Higuchi

Journal of Physics Conference SeriesMar 1, 20092 citations

Local Density Approximation for Superconductors

Stefan Kurth, Miguel A. L. Marques, Martin Lüders +1 more

Physical Review LettersSep 27, 199947 citations

Current-Density Functional Theory for the superconductor

Katsuhiko Higuchi, Masahiko Higuchi

arXiv:1610.00109Oct 1, 20160 citations

Computational pair density functional theory: A proposal for the kinetic energy functional

Katsuhiko Higuchi, Masahiko Higuchi

Physical Review BOct 22, 201026 citations

International Conference on Strongly Correlated Electron Systems (SCES)

A Calculation Scheme for the Pair-Density Functional Theory for the Superconductor

Katsuhiko Higuchi, Masahiko Higuchi

Published Mar 18, 2020• 1 citation

Publisher

Abstract

DOI: 10.7566/jpscp.30.011006

Related papers

Basic Variables to Be Reproduced in the First-Principles Theory for Superconductors: Fluctuation of the Particle Number

Katsuhiko Higuchi, Eina Miki, Masahiko Higuchi

We show that the diagonal elements of the second-order reduced density matrix (RDM2) can be chosen as basic variables for describing the superconducting state, instead of the off-diagonal elements of the RDM2 that are usually adopted as basic variables in the density functional scheme. The diagonal elements of the RDM2 are called pair-density (PD), which is explicitly related to the fluctuation of the particle number of the system. In this paper, we argue that the fluctuation of the particle number can become an indication of the superconducting state, and that the density functional scheme in which the PD is chosen as a basic variable would be a promising first-principles theory for superconductors.We show that the diagonal elements of the second-order reduced density matrix (RDM2) can be chosen as basic variables for describing the superconducting state, instead of the off-diagonal elements of the RDM2 that are usually adopted as basic variables in the density functional scheme. The diagonal elements of the RDM2 are called pair-density (PD), which is explicitly related to the fluctuation of the particle number of the system. In this paper, we argue that the fluctuation of the particle number can become an indication of the superconducting state, and that the density functional scheme in which the PD is chosen as a basic variable would be a promising first-principles theory for superconductors.

arXiv:1512.07775Journal of the Physical Society of JapanMay 11, 20179 citations

Pair density-functional theory by means of the correlated wave function

Masahiko Higuchi, Katsuhiko Higuchi

We present a density-functional scheme for calculating the pair density (PD) by means of the correlated wave function. The Jastrow wave function is adopted as the correlated wave function. By using the lowest-order approximation to the Jastrow wave function PDs, the search region for the ground-state PD is substantially extended as compared with our previous theory [Physica B 387, 117 (2007)]. The variational principle results in simultaneous equations that are practicable to calculate the ground-state PD.We present a density-functional scheme for calculating the pair density (PD) by means of the correlated wave function. The Jastrow wave function is adopted as the correlated wave function. By using the lowest-order approximation to the Jastrow wave function PDs, the search region for the ground-state PD is substantially extended as compared with our previous theory [Physica B 387, 117 (2007)]. The variational principle results in simultaneous equations that are practicable to calculate the ground-state PD.

arXiv:cond-mat/0610725Physical Review AApr 19, 200734 citations

A pair density functional theory utilizing the correlated wave function

Masahiko Higuchi, Katsuhiko Higuchi

We propose a practical scheme for calculating the ground-state pair density (PD) by utilizing the correlated wave function. As the correlated wave function, we adopt a linear combination of the single Slater determinants that are constructed from the solutions of the initial scheme[Higuchi M and Higuchi K 2007 Physica B 387 , 117]. The single-particle equation is derived by performing the variational principle within the set of PDs that are constructed from such correlated wave functions. Since the search region of the PD is substantially extended as compared with the initial scheme, it is expected that the present scheme can cover more correlation effects. The single-particle equation is practical, and may be easily applied to actual calculations.We propose a practical scheme for calculating the ground-state pair density (PD) by utilizing the correlated wave function. As the correlated wave function, we adopt a linear combination of the single Slater determinants that are constructed from the solutions of the initial scheme[Higuchi M and Higuchi K 2007 Physica B 387 , 117]. The single-particle equation is derived by performing the variational principle within the set of PDs that are constructed from such correlated wave functions. Since the search region of the PD is substantially extended as compared with the initial scheme, it is expected that the present scheme can cover more correlation effects. The single-particle equation is practical, and may be easily applied to actual calculations.

Journal of Physics Conference SeriesMar 1, 20092 citations

Local Density Approximation for Superconductors

Stefan Kurth, Miguel A. L. Marques, Martin Lüders +1 more

A universal LDA-type density functional describing the electronic correlations in superconductors is developed from first principles. The functional is constructed from the exchange-correlation free-energy density, ${f}_{\mathrm{xc}}^{\mathrm{hom}}$ , of a homogeneous electron gas exposed to an external translationally invariant pairing field. The quantity ${f}_{\mathrm{xc}}^{\mathrm{hom}}$ , which is a function of the density and a functional of the induced order parameter, is calculated by many-body perturbation theory.A universal LDA-type density functional describing the electronic correlations in superconductors is developed from first principles. The functional is constructed from the exchange-correlation free-energy density, ${f}_{\mathrm{xc}}^{\mathrm{hom}}$, of a homogeneous electron gas exposed to an external translationally invariant pairing field. The quantity ${f}_{\mathrm{xc}}^{\mathrm{hom}}$, which is a function of the density and a functional of the induced order parameter, is calculated by many-body perturbation theory.

Physical Review LettersSep 27, 199947 citations

Current-Density Functional Theory for the superconductor

Katsuhiko Higuchi, Masahiko Higuchi

We present the current-density functional theory for the superconductor immersed in the magnetic field. The order parameter of the superconducting state, transverse component of the paramagnetic current-density, and electron density are chosen as basic variables that uniquely determine the equilibrium properties of the system. In order to construct this theory, the development of the approximate form of the exchange-correlation (xc) energy functional is indispensable as well as the derivation of the effective single-particle equation which makes it possible to reproduce the equilibrium densities mentioned above. The rigorous expression of the xc-energy functional is derived using the technique of the coupling-constant integration. Furthermore, the approximate form of the xc energy functional is proposed such that the energy gap resulting from the effective single-particle equation is consistent with the attractive interaction energy of the system.We present the current-density functional theory for the superconductor immersed in the magnetic field. The order parameter of the superconducting state, transverse component of the paramagnetic current-density, and electron density are chosen as basic variables that uniquely determine the equilibrium properties of the system. In order to construct this theory, the development of the approximate form of the exchange-correlation (xc) energy functional is indispensable as well as the derivation of the effective single-particle equation which makes it possible to reproduce the equilibrium densities mentioned above. The rigorous expression of the xc-energy functional is derived using the technique of the coupling-constant integration. Furthermore, the approximate form of the xc energy functional is proposed such that the energy gap resulting from the effective single-particle equation is consistent with the attractive interaction energy of the system.

arXiv:1610.00109Oct 1, 20160 citations

Computational pair density functional theory: A proposal for the kinetic energy functional

Katsuhiko Higuchi, Masahiko Higuchi

We present a computational pair density (PD) functional theory using multiple Slater determinants in constructing the PD. Compared to the effective initial scheme [M. Higuchi and K. Higuchi, Phys. Rev. B 78, 125101 (2008)], the search region for the ground-state PD is substantially extended within the set of $N$ -representable PDs. The merit of the present scheme is to guarantee the resultant PD to be $N$ -representable and to describe correlation effects beyond the effective initial scheme, which enables us to tackle with the development of the approximate form of the kinetic energy functional. We derive two restrictive conditions on the kinetic energy functional. With the aid of these restrictive conditions, we also propose several types of approximate functionals of the kinetic energy. To check the abilities and limitations of the present scheme including such approximate functionals, actual calculations are performed for the neutral neon atom. The results show that the present scheme provides the $N$ -representable and correlated PDs, though it would have some limitations. What we need to do first for improvement of the computational PD functional theory is that the development of the approximate functional of the kinetic energy is further advanced along the present scheme.We present a computational pair density (PD) functional theory using multiple Slater determinants in constructing the PD. Compared to the effective initial scheme [M. Higuchi and K. Higuchi, Phys. Rev. B 78, 125101 (2008)], the search region for the ground-state PD is substantially extended within the set of $N$-representable PDs. The merit of the present scheme is to guarantee the resultant PD to be $N$-representable and to describe correlation effects beyond the effective initial scheme, which enables us to tackle with the development of the approximate form of the kinetic energy functional. We derive two restrictive conditions on the kinetic energy functional. With the aid of these restrictive conditions, we also propose several types of approximate functionals of the kinetic energy. To check the abilities and limitations of the present scheme including such approximate functionals, actual calculations are performed for the neutral neon atom. The results show that the present scheme provides the $N$-representable and correlated PDs, though it would have some limitations. What we need to do first for improvement of the computational PD functional theory is that the development of the approximate functional of the kinetic energy is further advanced along the present scheme.

Physical Review BOct 22, 201026 citations

{f}_{\mathrm{xc}}^{\mathrm{hom}}

, of a homogeneous electron gas exposed to an external translationally invariant pairing field. The quantity

{f}_{\mathrm{xc}}^{\mathrm{hom}}

, which is a function of the density and a functional of the induced order parameter, is calculated by many-body perturbation theory.

N

-representable PDs. The merit of the present scheme is to guarantee the resultant PD to be

N

-representable and to describe correlation effects beyond the effective initial scheme, which enables us to tackle with the development of the approximate form of the kinetic energy functional. We derive two restrictive conditions on the kinetic energy functional. With the aid of these restrictive conditions, we also propose several types of approximate functionals of the kinetic energy. To check the abilities and limitations of the present scheme including such approximate functionals, actual calculations are performed for the neutral neon atom. The results show that the present scheme provides the

N

-representable and correlated PDs, though it would have some limitations. What we need to do first for improvement of the computational PD functional theory is that the development of the approximate functional of the kinetic energy is further advanced along the present scheme.