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arXiv:cond-mat/0610725 · Physical Review A

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

Masahiko Higuchi, Katsuhiko Higuchi

Published Apr 19, 2007• 34 citations
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Abstract

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.

DOI
10.1103/physreva.75.042510

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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 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.
NNN-representability of the Jastrow wave function pair density of the lowest-order
We have recently proposed a density functional scheme for calculating the ground-state pair density (PD) within the Jastrow wave function PDs of the lowest-order (LO-Jastrow PDs) [M. Higuchi and K. Higuchi, Phys. Rev. A \textbf{75}, 042510 (2007)]. However, there remained an arguable problem on the NNN-representability of the LO-Jastrow PD. In this paper, the sufficient conditions for the NNN-representability of the LO-Jastrow PD are derived. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.
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 NNN-representable PDs. The merit of the present scheme is to guarantee the resultant PD to be NNN-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 NNN-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 study many-body correlations in the ground state of a general quantum system of bosons or fermions by including an additional Jastrow function in our recently proposed variational coupled-cluster method. Our approach combines the advantages of state-dependent correlations in the coupled-cluster theory and of the strong, short-ranged correlations of the Jastrow function. We apply a generalized linked-cluster expansion for the Jastrow wave function and provide a detailed analysis for practical evaluation of the Hamiltonian expectation value as an energy functional of the Jastrow function and the bare density-distribution functions introduced and calculated in our earlier publications; a simple, first-order energy functional is derived and detailed formulas for the higher-order contributions are provided. Our energy functional does not suffer the divergence as most coupled-cluster calculations often do when applying to Hamiltonians with hardcore potentials. We also discuss possible applications of our technique, including applications to strongly correlated fermion systems.
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.