Fluctuating parts of nuclear ground state correlation energies

Background: Heavy atomic nuclei are often described using the Hartree-Fock-Bogoliubov (HFB) method. In principle, this approach takes into account Pauli effects and pairing correlations while other correlation effects are mimicked through the use of effective density-dependent interactions. Purpose: Investigate the influence of higher order correlation effects on nuclear binding energies using Skyrme's effective interaction. Methods: A cut-off in relative momenta is introduced in order to remove ultraviolet divergences caused by the zero-range character of the interaction. Corrections to binding energies are then calculated using the quasiparticle-random-phase approximation (QRPA) and second order many-body perturbation theory (MBPT2). Result: Contributions to the correlation energies are evaluated for several isotopic chains and an attempt is made to disentangle which parts give rise to fluctuations that may be difficult to incorporate on the HFB level. The dependence of the results on the cut-off is also investigated. Conclusions: The improved interaction allows explicit summations of perturbation series which is useful for the description of some nuclear observables. However, refits of the interaction parameters are needed to obtain more quantitative results

Calculations of Hubbard U from first-principles

The Hubbard \emph{U} of the \emph{3d} transition metal series as well as SrVO$_{3}$, YTiO$_{3}$, Ce and Gd has been estimated using a recently proposed scheme based on the random-phase approximation. The values obtained are generally in good accord with the values often used in model calculations but for some cases the estimated values are somewhat smaller than those used in the literature. We have also calculated the frequency-dependent \emph{U} for some of the materials. The strong frequency dependence of \emph{U} in some of the cases considered in this paper suggests that the static value of \emph{U} may not be the most appropriate one to use in model calculations. We have also made comparison with the constrained LDA method and found some discrepancies in a number of cases. We emphasize that our scheme and the constrained LDA method theoretically ought to give similar results and the discrepancies may be attributed to technical difficulties in performing calculations based on currently implemented constrained LDA schemes.Comment: 24 pages, 13 figures; Submitted to Phys. Rev.

The correlation potential in density functional theory at the GW-level: spherical atoms

As part of a project to obtain better optical response functions for nano materials and other systems with strong excitonic effects we here calculate the exchange-correlation (XC) potential of density-functional theory (DFT) at a level of approximation which corresponds to the dynamically- screened-exchange or GW approximation. In this process we have designed a new numerical method based on cubic splines which appears to be superior to other techniques previously applied to the "inverse engineering problem" of DFT, i.e., the problem of finding an XC potential from a known particle density. The potentials we obtain do not suffer from unphysical ripple and have, to within a reasonable accuracy, the correct asymptotic tails outside localized systems. The XC potential is an important ingredient in finding the particle-conserving excitation energies in atoms and molecules and our potentials perform better in this regard as compared to the LDA potential, potentials from GGA:s, and a DFT potential based on MP2 theory.Comment: 13 pages, 9 figure

A simple, efficient, and general treatment of the singularities in Hartree-Fock and exact-exchange Kohn-Sham methods for solids

We present a general scheme for treating the integrable singular terms within exact exchange (EXX) Kohn-Sham or Hartree-Fock (HF) methods for periodic solids. We show that the singularity corrections for treating these divergencies depend only on the total number and the positions of k-points and on the lattice vectors, in particular the unit cell volume, but not on the particular positions of atoms within the unit cell. The method proposed here to treat the singularities constitutes a stable, simple to implement, and general scheme that can be applied to systems with arbitrary lattice parameters within either the EXX Kohn-Sham or the HF formalism. We apply the singularity correction to a typical symmetric structure, diamond, and to a more general structure, trans-polyacetylene. We consider the effect of the singularity corrections on volume optimisations and k-point convergence. While the singularity corrections clearly depends on the total number of k-points, it exhibits a remarkably small dependence upon the choice of the specific arrangement of the k-points.Comment: 24 pages, 5 Figures, re-submitted to Phys. Rev. B after revision

Edge states of zigzag bilayer graphite nanoribbons

Electronic structures of the zigzag bilayer graphite nanoribbons(Z-BGNR) with various ribbon width $N$ are studied within the tight binding approximation. Neglecting the inter-layer hopping amplitude $\gamma_4$, which is an order of magnitude smaller than the other inter-layer hopping parameters $\gamma_1$ and $\gamma_3$, there exist two fixed Fermi points $\pm k^*$ independent of the ribbon width with the peculiar energy dispersion near $k^*$ as \ve (k) \sim \pm (k-k^*)^N. By investigating the edge states of the Z-BGNR, we notice that the trigonal warping of the bilayer graphene sheets are reflected on in the edge state structure. With the inclusion of $\gamma_4$, the above two Fermi points are not fixed, but drift toward the vicinity of the Dirac point with the increase of the width $N$ as shown by the finite scaling method and the peculiar dispersions change to the parabolic ones. The edge magnetism of the Z-BGNR is also examined by solving the half-filled Hubbard Hamiltonian for the ribbon using the Hartree-Fock approximation. We have shown that within the same side of the edges, the edge spins are aligned ferromagnetically for the experimentally relevant set of parameters.Comment: 22 pages, 7 figures; Corrections are added concerning the edge magnetis

Electric field response of strongly correlated one-dimensional metals: a Bethe-Ansatz density functional theory study

We present a theoretical study on the response properties to an external electric field of strongly correlated one-dimensional metals. Our investigation is based on the recently developed Bethe-Ansatz local density approximation (BALDA) to the density functional theory formulation of the Hubbard model. This is capable of describing both Luttinger liquid and Mott-insulator correlations. The BALDA calculated values for the static linear polarizability are compared with those obtained by numerically accurate methods, such as exact (Lanczos) diagonalization and the density matrix renormalization group, over a broad range of parameters. In general BALDA linear polarizabilities are in good agreement with the exact results. The response of the exact exchange and correlation potential is found to point in the same direction of the perturbing potential. This is well reproduced by the BALDA approach, although the fine details depend on the specific parameterization for the local approximation. Finally we provide a numerical proof for the non-locality of the exact exchange and correlation functional.Comment: 8 pages and 8 figure

GW band structure of InAs and GaAs in the wurtzite phase

We report the first quasiparticle calculations of the newly observed wurtzite polymorph of InAs and GaAs. The calculations are performed in the GW approximation using plane waves and pseudopotentials. For comparison we also report the study of the zinc-blende phase within the same approximations. In the InAs compound the In 4d electrons play a very important role: whether they are frozen in the core or not, leads either to a correct or a wrong band ordering (negative gap) within the Local Density Appproximation (LDA). We have calculated the GW band structure in both cases. In the first approach, we have estimated the correction to the pd repulsion calculated within the LDA and included this effect in the calculation of the GW corrections to the LDA spectrum. In the second case, we circumvent the negative gap problem by first using the screened exchange approximation and then calculating the GW corrections starting from the so obtained eigenvalues and eigenfunctions. This approach leads to a more realistic band-structure and was also used for GaAs. For both InAs and GaAs in the wurtzite phase we predict an increase of the quasiparticle gap with respect to the zinc-blende polytype.Comment: 9 pages, 6 figures, 3 table

Optimized Effective Potential Model for the Double Perovskites Sr2-xYxVMoO6 and Sr2-xYxVTcO6

In attempt to explore half-metallic properties of the double perovskites Sr2-xYxVMoO6 and Sr2-xYxVTcO6, we construct an effective low-energy model, which describes the behavior of the t2g-states of these compounds. All parameters of such model are derived rigorously on the basis of first-principles electronic structure calculations. In order to solve this model we employ the optimized effective potential method and treat the correlation interactions in the random phase approximation. Although correlation interactions considerably reduce the intraatomic exchange splitting in comparison with the Hartree-Fock method, this splitting still substantially exceeds the typical values obtained in the local-spin-density approximation (LSDA), which alters many predictions based on the LSDA. Our main results are summarized as follows: (i) all ferromagnetic states are expected to be half-metallic. However, their energies are generally higher than those of the ferrimagnetic ordering between V- and Mo/Tc-sites (except Sr2VMoO6); (ii) all ferrimagnetic states are metallic (except fully insulating Y2VTcO6) and no half-metallic antiferromagnetism has been found; (iii) moreover, many of the ferrimagnetic structures appear to be unstable with respect to the spin-spiral alignment. Thus, the true magnetic ground state of the most of these systems is expected to be more complex. In addition, we discuss several methodological issues related to the nonuniqueness of the effective potential for the magnetic half-metallic and insulating states.Comment: 15 pages, 9 figure

First principles studies of modulated Co/Cu superlattices with strongly and weakly exchange biased Co-monolayers

First-principles calculations have been performed in order to determine effective exchange integrals between {\it strongly} and {\it weakly} exchange-coupled Co monolayers in certain modulated periodic $CoCu_2/CoCu_n$-type superlattices with three non-equivalent Co planes, which have not yet been studied hitherto. For $3\le n\le 6$ we find that the two non-equivalent exchange integrals have opposite signs, i.e.~the strong coupling is antiferromagnetic and the weak coupling ferromagnetic, and differ for $n\ne 4$ from each other by one order of magnitude. It is shown that the results depend on the system as a whole and could not be obtained from separate parts. Finally we suggest that ''spin valve'' systems of such kind should be considered when trying to obtain good magneto-resistance together with low switching-fields.Comment: LaTex, 9 pages, including two .eps-figure