Systematic generation of finite-range atomic basis sets for linear-scaling calculations

Basis sets of atomic orbitals are very efficient for density functional calculations but lack a systematic variational convergence. We present a variational method to optimize numerical atomic orbitals using a single parameter to control their range. The efficiency of the basis generation scheme is tested and compared with other schemes for multiple zeta basis sets. The scheme shows to be comparable in quality to other widely used schemes albeit offering better performance for linear-scaling computations

Symplectic Symmetry of the Neutrino Mass and the See-Saw Mechanism

We investigate the algebraic structure of the most general neutrino mass Hamiltonian and place the see-saw mechanism in an algebraic framework. We show that this Hamiltonian can be written in terms of the generators of an Sp(4) algebra. The Pauli-Gursey transformation is an SU(2) rotation which is embedded in this Sp(4) group. This SU(2) also generates the see-saw mechanism.Comment: 11 pages, REVTE

Fuzzy Scalar Field Theory as a Multitrace Matrix Model

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Such a model can be solved by standard techniques as e.g. the saddle-point approximation. We evaluate the perturbative expansion up to second order and present the one-cut solution of the saddle-point approximation in the large N limit. We apply our approach to a model which has been proposed as an appropriate regularization of scalar field theory on the plane within the framework of fuzzy geometry.Comment: 1+25 pages, replaced with published version, minor improvement

Structural and superconducting transition in selenium under high pressures

First-principles calculations are performed for electronic structures of two high pressure phases of solid selenium, $\beta$-Po and bcc. Our calculation reproduces well the pressure-induced phase transition from $\beta$-Po to bcc observed in selenium. The calculated transition pressure is 30 GPa lower than the observed one, but the calculated pressure dependence of the lattice parameters agrees fairly well with the observations in a wide range of pressure. We estimate the superconducting transition temperature $T_{\rm c}$ of both the $\beta$-Po and the bcc phases by calculating the phonon dispersion and the electron-phonon interaction on the basis of density-functional perturbation theory. The calculated $T_{\rm c}$ shows a characteristic pressure dependence, i.e. it is rather pressure independent in the $\beta$-Po phase, shows a discontinuous jump at the transition from $\beta$-Po to bcc, and then decreases rapidly with increasing pressure in the bcc phase.Comment: 8 pages, 11 figure

The diagonalization method in quantum recursion theory

As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.Comment: 15 pages, completely rewritte

Investigation of the Jahn-Teller Transition in TiF3 using Density Functional Theory

We use first principles density functional theory to calculate electronic and magnetic properties of TiF3 using the full potential linearized augmented plane wave method. The LDA approximation predicts a fully saturated ferromagnetic metal and finds degenerate energy minima for high and low symmetry structures. The experimentally observed Jahn-Teller phase transition at Tc=370K can not be driven by the electron-phonon interaction alone, which is usually described accurately by LDA. Electron correlations beyond LDA are essential to lift the degeneracy of the singly occupied Ti t2g orbital. Although the on-site Coulomb correlations are important, the direction of the t2g-level splitting is determined by the dipole-dipole interactions. The LDA+U functional predicts an aniferromagnetic insulator with an orbitally ordered ground state. The input parameters U=8.1 eV and J=0.9 eV for the Ti 3d orbital were found by varying the total charge on the TiF$_6^{2-}$ ion using the molecular NRLMOL code. We estimate the Heisenberg exchange constant for spin-1/2 on a cubic lattice to be approximately 24 K. The symmetry lowering energy in LDA+U is about 900 K per TiF3 formula unit.Comment: 7 pages, 9 figures, to appear in Phys. Rev.

Use of the Generalized Gradient Approximation in Pseudopotential Calculations of Solids

We present a study of the equilibrium properties of $sp$-bonded solids within the pseudopotential approach, employing recently proposed generalized gradient approximation (GGA) exchange correlation functionals. We analyze the effects of the gradient corrections on the behavior of the pseudopotentials and discuss possible approaches for constructing pseudopotentials self-consistently in the context of gradient corrected functionals. The calculated equilibrium properties of solids using the GGA functionals are compared to the ones obtained through the local density approximation (LDA) and to experimental data. A significant improvement over the LDA results is achieved with the use of the GGA functionals for cohesive energies. For the lattice constant, the same accuracy as in LDA can be obtained when the nonlinear coupling between core and valence electrons introduced by the exchange correlation functionals is properly taken into account. However, GGA functionals give bulk moduli that are too small compared to experiment.Comment: 15 pages, latex, no figure

Reversible Pressure-Induced Amorphization in Solid C70 : Raman and Photoluminescence Study

We have studied single crystals of $C_{70}$ by Raman scattering and photoluminescence in the pressure range from 0 to 31.1 GPa. The Raman spectrum at 31.1 GPa shows only a broad band similar to that of the amorphous carbon without any trace of the Raman lines of $C_{70}$. After releasing the pressure from 31.1 GPa, the Raman and the photoluminescence spectra of the recovered sample are that of the starting $C_{70}$ crystal. These results indicate that the $C_{70}$ molecules are stable upto 31.1 GPa and the amorphous carbon high pressure phase is reversible, in sharp contrast to the results on solid $C_{60}$. A qualitative explaination is suggested in terms of inter- versus intra-molecular interactions.Comment: To appear in Phys. Rev. Lett., 12 pages, RevTeX (preprint format), 3 figures available upon reques

First-principles study of the ferroelastic phase transition in CaCl_2

First-principles density-functional calculations within the local-density approximation and the pseudopotential approach are used to study and characterize the ferroelastic phase transition in calcium chloride (CaCl_2). In accord with experiment, the energy map of CaCl_2 has the typical features of a pseudoproper ferroelastic with an optical instability as ultimate origin of the phase transition. This unstable optic mode is close to a pure rigid unit mode of the framework of chlorine atoms and has a negative Gruneisen parameter. The ab-initio ground state agrees fairly well with the experimental low temperature structure extrapolated at 0K. The calculated energy map around the ground state is interpreted as an extrapolated Landau free-energy and is successfully used to explain some of the observed thermal properties. Higher-order anharmonic couplings between the strain and the unstable optic mode, proposed in previous literature as important terms to explain the soft-phonon temperature behavior, are shown to be irrelevant for this purpose. The LAPW method is shown to reproduce the plane-wave results in CaCl_2 within the precision of the calculations, and is used to analyze the relative stability of different phases in CaCl_2 and the chemically similar compound SrCl_2.Comment: 9 pages, 6 figures, uses RevTeX