We have extended the momentum-dependent local-ansatz (MLA) wavefunction method to the first-principles version using the tight-binding LDA+U Hamiltonian for the description of correlated electrons in the real system. The MLA reduces to the Rayleigh-Schrödinger perturbation theory in the weak correlation limit, and describes quantitatively the ground state and related low-energy excitations in solids. The theory has been applied to the paramagnetic Fe. The role of electron correlations on the energy, charge fluctuations, amplitude of local moment, momentum distribution functions, as well as the mass enhancement factor in Fe has been examined as a function of Coulomb interaction strength. It is shown that the inter-orbital charge-charge correlations between d electrons make a significant contribution to the correlation energy and charge fluctuations, while the intra-orbital and inter-orbital spin-spin correlations make a dominant contribution to the amplitude of local moment and the mass enhancement in Fe. Calculated partial mass enhancements are found to be 1.01, 1.01, and 3.33 for s, p, and d electrons, respectively. The averaged mass enhancement 1.65 is shown to be consistent with the experimental data as well as the recent results of theoretical calculations.

We have developed a first-principles local ansatz wavefunction approach with momentum-dependent variational parameters on the basis of the tight-binding LDA+U Hamiltonian. The theory goes beyond the first-principles Gutzwiller approach and quantitatively describes correlated electron systems. Using the theory, we find that the momentum distribution function (MDF) bands of paramagnetic bcc Fe along highsymmetry lines show a large deviation from the Fermi-Dirac function for the d electrons with e g symmetry and yield the momentum-dependent mass enhancement factors. The calculated average mass enhancement m * /m = 1.65 is consistent with low-temperature specific heat data as well as recent angle-resolved photoemission spectroscopy (ARPES) data. The quantitative description of correlated electrons in solids has been one of the central issues in condensed matter physics. Band theory has been developed towards such a quantitative description by taking into account electron-electron interactions. Density functional theory (DFT) is the state-of-the-art theory along this line. The DFT is based on the Hohenberg-Kohn theorem 1) and the Kohn-Sham method. 2) The local density approximation (LDA) and the generalized gradient approximation (GGA) to the exchange correlation potential led to the development of the DFT as a quantitative theory.Although the DFT has been successful for the quantitative understanding of metals and band insulators, it has failed to provide a quantitative description of more correlated electron systems such as ǫ-Fe, 3) Fe pnictides, 4) cuprates, 5) as well as heavy-fermion * E-mail address: yok@sci.u-ryukyu.ac.jp, be published in J. Phys. Soc. Jpn. 85 (2016).

The wavefunction method provides us with a useful tool to describe electron correlations in solids at the ground state. In this paper we review the recent development of the momentum-dependent local ansatz wavefunction (MLA). It is constructed by taking into account two-particle excited states projected onto the local orbitals, and the momentum-dependent amplitudes of these states are chosen as variational parameters. The MLA describes accurately correlated electron states from the weak to the intermediate Coulomb interaction regime in infinite dimensions, and works well even in the strongly correlated region by introducing a new starting wavefunction called the hybrid (HB) wavefunction. The MLA-HB is therefore shown to overcome the limitation of the original local ansatz (LA) wavefunction as well as the Gutzwiller wavefunction. In particular, the calculated quasiparticle weight vs Coulomb interaction curve is shown to be close to that obtained by the numerical renormalization group approach. It is also shown that the MLA is applicable to the first-principles Hamiltonian.Comment: 32 pages, 7 figure

The momentum distribution function (MDF) bands of iron-group transition metals from Sc to Cu have been investigated on the basis of the first-principles momentum dependent local ansatz wavefunction method. It is found that the MDF for d electrons show a strong momentum dependence and a large deviation from the Fermi-Dirac distribution function along high-symmetry lines of the first Brillouin zone, while the sp electrons behave as independent electrons. In particular, the deviation in bcc Fe (fcc Ni) is shown to be enhanced by the narrow e g (t 2g ) bands with flat dispersion in the vicinity of the Fermi level. Mass enhancement factors (MEF) calculated from the jump on the Fermi surface are also shown to be momentum dependent. Large mass enhancements of Mn and Fe are found to be caused by spin fluctuations due to d electrons, while that for Ni is mainly caused by charge fluctuations. Calculated MEF are consistent with electronic specific heat data as well as the recent angle resolved photoemission spectroscopy data.

The ground-state properties of iron-group transition metals from Sc to Cu have been investigated on the basis of the first-principles momentum dependent local ansatz (MLA) theory. Correlation energy gain is found to show large values for Mn and Fe: 0.090 Ry (Mn) and 0.094 Ry (Fe). The Hund-rule coupling energies are found to be 3000 K (Fe), 1400 K (Co), and 300 K (Ni). It is sugested that these values can resolve the inconsistency in magnetic energy between the density functional theory and the first-principles dynamical coherent potential approximation theory at finite temperatures. Charge fluctuations are shown to be suppressed by the intra-orbital correlations and inter-orbital charge-charge correlations, so that they show nearly constant values from V to Fe: 1.57 (V and Cr), 1.52 (Mn), and 1.44 (Fe), which are roughly twice as large as those obtained by the d band model. The amplitudes of local moments are enhanced by the intra-orbital and inter-orbital spin-spin correlations and show large values for Mn and Fe: 2.87 (Mn) and 2.58 (Fe). These values are in good agreement with the experimental values estimated from the effective Bohr magneton number and the inner core photoemission data. KEYWORDS: first-principles variational theory, momentum-dependent local ansatz, iron-group transition metals, electron correlations, correlation energy, charge fluctuations, amplitude of local moment * yok@sci.u-ryukyu.ac.jp, to be published in J. Phys. Soc. Jpn. 85 (2016).