Monte Carlo Simulations with Indefinite and Complex-Valued Measures

A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. Exactly solvable, one-dimensional Ising models with complex temperature and complex activity illustrate the considerable improvements and the workability of the new method even when the crude one fails.Comment: 10 A4 pages, postscript (140K), UM-P-93-7

An exchange-correlation energy for a two-dimensional electron gas in a magnetic field

We present the results of a variational Monte Carlo calculation of the exchange-correlation energy for a spin-polarized two-dimensional electron gas in a perpendicular magnetic field. These energies are a necessary input to the recently developed current-density functional theory. Landau-level mixing is included in a variational manner, which gives the energy at finite density at finite field, in contrast to previous approaches. Results are presented for the exchange-correlation energy and excited-state gap at $\nu =$ 1/7, 1/5, 1/3, 1, and 2. We parameterize the results as a function of $r_s$ and $\nu$ in a form convenient for current-density functional calculations.Comment: 36 pages, including 6 postscript figure

Equation of state and phonon frequency calculations of diamond at high pressures

The pressure-volume relationship and the zone-center optical phonon frequency of cubic diamond at pressures up to 600 GPa have been calculated based on Density Functional Theory within the Local Density Approximation and the Generalized Gradient Approximation. Three different approaches, viz. a pseudopotential method applied in the basis of plane waves, an all-electron method relying on Augmented Plane Waves plus Local Orbitals, and an intermediate approach implemented in the basis of Projector Augmented Waves have been used. All these methods and approximations yield consistent results for the pressure derivative of the bulk modulus and the volume dependence of the mode Grueneisen parameter of diamond. The results are at variance with recent precise measurements up to 140 GPa. Possible implications for the experimental pressure determination based on the ruby luminescence method are discussed.Comment: 10 pages, 6 figure

Electron correlations for ground state properties of group IV semiconductors

Valence energies for crystalline C, Si, Ge, and Sn with diamond structure have been determined using an ab-initio approach based on information from cluster calculations. Correlation contributions, in particular, have been evaluated in the coupled electron pair approximation (CEPA), by means of increments obtained for localized bond orbitals and for pairs and triples of such bonds. Combining these results with corresponding Hartree-Fock (HF) data, we recover about 95 % of the experimental cohesive energies. Lattice constants are overestimated at the HF level by about 1.5 %; correlation effects reduce these deviations to values which are within the error bounds of this method. A similar behavior is found for the bulk modulus: the HF values which are significantly too high are reduced by correlation effects to about 97 % of the experimental values.Comment: 22 pages, latex, 2 figure

Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon

Quantum Monte Carlo (QMC) techniques are used to calculate the one-body density matrix and excitation energies for the valence electrons of bulk silicon. The one-body density matrix and energies are obtained from a Slater-Jastrow wave function with a determinant of local density approximation (LDA) orbitals. The QMC density matrix evaluated in a basis of LDA orbitals is strongly diagonally dominant. The natural orbitals obtained by diagonalizing the QMC density matrix resemble the LDA orbitals very closely. Replacing the determinant of LDA orbitals in the wave function by a determinant of natural orbitals makes no significant difference to the quality of the wave function's nodal surface, leaving the diffusion Monte Carlo energy unchanged. The Extended Koopmans' Theorem for correlated wave functions is used to calculate excitation energies for silicon, which are in reasonable agreement with the available experimental data. A diagonal approximation to the theorem, evaluated in the basis of LDA orbitals, works quite well for both the quasihole and quasielectron states. We have found that this approximation has an advantageous scaling with system size, allowing more efficient studies of larger systems.Comment: 13 pages, 4 figures. To appear in Phys. Rev.

Theoretical evidences for enhanced superconducting transition temperature of CaSi2_2 in a high-pressure AlB2_2 phase

By means of first-principles calculations, we studied stable lattice structures and estimated superconducting transition temperature of CaSi$_2$ at high pressure. Our simulation showed stability of the AlB$_2$ structure in a pressure range above 17 GPa. In this structure, doubly degenerated optical phonon modes, in which the neighboring silicon atoms oscillate alternately in a silicon plane, show prominently strong interaction with the conduction electrons. In addition there exists a softened optical mode (out-of-plan motion of silicon atoms), whose strength of the electron-phonon interaction is nearly the same as the above mode. The density of states at the Fermi level in the AlB$_2$ structure is higher than that in the trigonal structure. These findings and the estimation of the transition temperature strongly suggest that higher $T_{\rm c}$ is expected in the AlB$_2$ structure than the trigonal structures which are known so far.Comment: 6 pages and 11 figure

Correlation effects in MgO and CaO: Cohesive energies and lattice constants

A recently proposed computational scheme based on local increments has been applied to the calculation of correlation contributions to the cohesive energy of the CaO crystal. Using ab-initio quantum chemical methods for evaluating individual increments, we obtain 80% of the difference between the experimental and Hartree-Fock cohesive energies. Lattice constants corrected for correlation effects deviate by less than 1% from experimental values, in the case of MgO and CaO.Comment: LaTeX, 4 figure