Showing papers on "Random phase approximation published in 1993"

Superfluid and insulating phases in an interacting-boson model: mean-field theory and the RPA

Abstract: The bosonic Hubbard model is studied via a simple mean-field theory. At zero temperature, in addition to yielding a phase diagram that is qualitatively correct, namely a superfluid phase for non-integer fillings and a Mott transition from a superfluid to an insulating phase for integer fillings, this theory gives results that are in good agreement with Monte Carlo simulations. In particular, the superfluid fraction obtained as a function of the interaction strength U for both integer and non-integer fillings is close to the simulation results. In all phases the excitation spectra are obtained by using the random phase approximation (RPA): the spectrum has a gap in the insulating phase and is gapless (and linear at small wave vectors) in the superfluid phase. Analytic results are presented in the limits of large U and small superfluid density. Finite-temperature phase diagrams and the Mott-insulator-normal-phase crossover are also described.

Optical properties of semiconductors within the independent-quasiparticle approximation.

Abstract: We develop a gauge-invariant formalism for calculating the optical properties of solids within the random-phase approximation and the GW approach to electron bands (the independent-quasiparticle approximation). We show that, within the scissors-operator approximation, it is enough to shift rigidly the optical spectrum, calculated according to the density-functional theory--local-density approximation, to higher energies by the gap correction. Moreover, a simple formula is given valid beyond the scissors-operator approximation.

A direct algorithm for self‐consistent‐field linear response theory and application to C60: Excitation energies, oscillator strengths, and frequency‐dependent polarizabilities

Abstract: We present a direct self‐consistent‐field (SCF)‐type algorithm and its implementation for the computation of linear response properties: excitation energies, oscillator strengths, and frequency‐dependent polarizabilities within the time‐dependent SCF or random phase approximation. The treatment of singles configuration interaction for electronic excitations and Hartree–Fock instability criteria are covered as special cases. The algorithm is based on proven direct SCF methodology. This, together with full exploitation of molecular symmetry, opens the way to the treatment of large molecules. Applications to C60 strongly support the assignment of the lowest‐lying dipole allowed transition to the strong band at 3.8 eV.

Model dielectric function for semiconductors.

Abstract: We present a model for the dielectric function of semiconductors. It has been tested successfully for Si, Ge, GaAs, and ZnSe. In conjunction with the single plasmon-pole approximation it yields plasmon-energy dispersions in fair agreement with experiments. It allows one, moreover, to deduce an analytical expression for the Coulomb-hole part of the static self-energy operator.

Optical response of large lithium clusters: Evolution toward the bulk.

Abstract: Multistep photon absorption has been used to measure the collective excitation of free lithium clusters having up to 1500 atoms. The blueshift of the Mie resonance energy, as cluster size increases, probes the surface erects. Its absolute value is consistent with the dielectric constants of the bulk down to a 100 atom cluster. The comparison with calculations in random-phase approximation in the local approximation demonstrates that the jellium model is no longer valid for lithium clusters

Evolution of the optical properties of alkali-metal microclusters towards the bulk: The matrix random-phase-approximation description.

Abstract: The evolution toward the bulk values of the energy centroid and of the width characterizing the surface-plasmon resonance in spherical neutral sodium clusters is studied. For this purpose, the photoabsorption spectrum of clusters comprising from 8 to 338 atoms is calculated microscopically making use of the jellium shell model to describe the motion of delocalised electrons and of the matrix random-phase approximation to determine the collective response of the system to electromagnetic radiation. The Coulomb force is treated in the local-density approximation. The case of large potassium clusters having approximately 500 and 900 atoms is also considered

Møller–Plesset expansion of the dispersion energy in the ring approximation

Abstract: Coupled-cluster equations for the calculation of the nonexpanded (fully damped) dispersion energy are derived. These equations are solved in the ring approximation using the Moller–Plesset expansion in terms of the fluctuation potentials WA and WB for the individual molecules. Numerical results of high-order perturbative calculations for the He, H2, LiH, H2O, and HF dimers are presented and compared with the converged results computed using the same basis sets. It is found that the convergence of the Moller-Plesset expansion of the dispersion energy in the ring approximation is very fast. The pade approximants still accelerate this already good convergence. For all complexes studied in this paper, the sum of the corrections through the second-order in WA + WB reproduces over 99% of the converged value. The sum of third- and higher-order corrections in the ring approximation is found to be one or two orders of magnitude smaller than the sum of second-order terms not included in the ring approximation and, therefore, may be safely neglected. Thus, it appears that a second-order calculation, which does not require iterating coupled-cluster equations or solving random phase approximation equations, offers the best compromise between accuracy and computational requirements. © 1993 John Wiley & Sons, Inc.

Exotic behavior of the dielectric function and the plasmons of an electron gas on a tubule.

Abstract: The dielectric response of an electron gas confined to the surface of a hollow infinitely long cylinder is calculated in the random-phase approximation. The frequency dependence of the imaginary part of the dielectric function shows a steplike behavior. The dielectric function shows the dimensional crossover from two-dimensional to one-dimensional behavior with decreasing cylinder radius. In the quasi-one-dimensional case, our model does not need any artificial cutoff parameters for the Coulomb potential.

Finite-wave-vector electromagnetic response of fractional quantized Hall states.

Abstract: A fractional quantized Hall state with filling fraction \ensuremath{ u}=p/(2mp+1) can be modeled as an integer quantized Hall state of transformed fermions, interacting with a Chern-Simons field. The electromagnetic response function for these states at arbitrary frequency and wave vector can be calculated using a semiclassical approximation or the random-phase approximation. However, such calculations do not properly take into account the large effective-mass renormalization which is present in the Chern-Simons theory. We show how the mass renormalization can be incorporated in a calculation of the response function within a Landau-Fermi-liquid theory approach such that Kohn's theorem and the f-sum rules are properly satisfied. We present results of such calculations.

s- and p-wave pairings in the dilute electron gas: Superconductivity mediated by the Coulomb hole in the vicinity of the Wigner-crystal phase.

Abstract: The superconducting transition temperature T c of both s- and p-wave pairings is calculated in the electron gas without phonons by the solution of the full Eliashberg equation in both frequency and momentum variables. The exchange and correlation effects are included in the form of the model proposed by Kukkonen and Overhauser with suitable local-field corrections. The ground state of the electron gas exhibits p-wave superconductivity for the electronic-density parameter r s around 4 or larger, but it is superseded by s-wave superconductivity for r s larger than about 8.5

Surface wake in the random-phase approximation

Abstract: The scalar-electric-potential distribution set up by an ion traveling in the vicinity of a plane solid-vacuum interface, that is, the surface-wake potential, is investigated with the specular-reflection model to describe the response of the surface and with the random-phase approximation for the dielectric function of the bulk material. This permits us to address the study of the low-velocity surface wake: the static potential is found to have a dip at the position of the ion; that dip is shifted towards the direction opposite to the velocity vector for velocities smaller than the threshold of creation of plasmons (\ensuremath{\approxeq}1.3${\mathit{v}}_{\mathit{F}}$). Extensive numerical calculations are presented for an ion both inside and outside aluminum. Comparison to the results obtained with the plasmon-pole dielectric function indicates excellent agreement for velocities larger than \ensuremath{\approxeq}1.3${\mathit{v}}_{\mathit{F}}$. On the other side, the possibility of surface-wake riding is suggested, by analogy with bulk-wake riding postulated in the past. In it, the electron would be bound in the first trough of the surface-wake potential set up when the ion describes a grazing trajectory. The main feature introduced by the surface with respect to the bulk consists of allowing the use of ions of higher charge, reducing in this way the relative importance of the electron self-energy, and in addition, giving rise to larger binding energies. When the ion beam is directed along a special direction of an oriented crystal surface, the mechanism of resonant coherent excitation could provide a way for experimentally detecting this phenomenon through the emission of the bound electron with well-defined energy and around a preferential direction.

Relativistic excitation energies and oscillator strengths including core-polarization effects for the intercombination and resonance transitions in Mg-like ions

Abstract: Excitation energies and oscillator strengths from the 1S0 ground state to the first 3P10 and 1P10 excited states of Mg-like ions are calculated using the multiconfiguration relativistic random-phase approximation including excitation channels from core electrons. The discrepancies between the relativistic random-phase approximation calculation and experimental results for the intercombination excitation energies and oscillator strengths are much reduced. The excitation energies and oscillator strengths for the resonance transition from the multiconfiguration relativistic random-phase approximation are in excellent agreement with experiment. A substantial part of the discrepancy in the 3P10-1P10 separations is resolved when core excitation channels are taken into account.

Coulomb coupling between spatially separated electron and hole layers : generalized random-phase approximation

Abstract: Coulomb coupling between spatially separated quasi-two-dimensional electron and hole gases is studied as a function of temperature and/or electron (hole) gas density. Because of the exclusion principle mainly electrons and holes of antiparallel spin screen the electron-hole interaction at low densities. The coupling is described by a generalized random-phase approximation which takes into account exchange processes to all orders of the Hartree-Fock potential. The temperature dependence of the transimpedance agrees very well with experiment for relatively high densities; its density dependence agrees well for high densities and reasonably well for low and intermediate densities.

Screening of the electron-phonon interaction in quasi-one-dimensional semiconductor structures.

Abstract: The screening of the electron-phonon interaction due to a quasi-one-dimensional (Q1D) electron gas is investigated. The contribution of the electron-phonon interaction to the ground-state energy of the Q1D polaron gas in different semiconductor quantum-well-wire structures is calculated within the Hartree-Fock and the random-phase approximation. The influences of the width of the quantum-well wire and the electron density on the ground-state energy of the polaron gas are studied. We found that the screening due to the electron gas reduces the effective electron-phonon coupling in a Q1D system appreciably and the contribution of the electron-phonon interaction to the ground-state energy of the polaron gas decreases with increasing electron density

Dynamic structure of electrons in Al metal studied by inelastic x-ray scattering.

Abstract: The dynamic structure factor S(q,\ensuremath{\omega}) of electrons in single-crystal Al metal was measured with 1.4-eV resolution by means of inelastic x-ray-scattering spectroscopy for q parallel to [100] and for q parallel to [110] with 0.37q2.06 a.u. using synchrotron radiation from DORIS storage ring. The overall shape of the experimental dynamic structure factors is in agreement with jellium calculations which extend the random-phase approximation by taking into account both local-field corrections and the influence of the momentum-dependent lifetime of the quasiparticles. Besides some q-orientation-dependent fine structure, the S(q,\ensuremath{\omega}) spectra for qg1.1 a.u. exhibit a q-orientation-independent double-peak or one-peak--one-shoulder fine structure. Whereas the q-orientation-dependent fine structure can be attributed to ion-lattice-induced indentations in the electron-hole excitation continuum due to Bragg reflections, the origin of the q-orientation-independent fine structure could not be clarified definitively. The most probable explanation of this fine structure which is based on semiquantitative agreement with model calculations is the shifting down of unoccupied d-like bands due to the lack of d core-state orthogonalization. Alternative interpretations on the basis of special features of the short-range electron correlations (lifetime effects, multiple-pair excitation, plasmaron ground state) have either failed or have been left on the level of qualitative and somewhat speculative arguments.

Optical conductivity of la2-xsrxcuo4 and soft electronic-modes

Abstract: We calculate the optical conductivity of La2-xSrxCuO4 in the inhomogeneous Hartree-Fock plus random phase approximation using the p-d model with parameters taken from first-principles calculations. The ground state evolves from a polaron state for small and moderate doping to a conventional metal for x greater than or similar to 1/4 in consistency with transport and optical experiments. The calculated optical conductivity shows good agreement with experiments regarding the peak positions and relative intensities for zero and small dopings. The precursor of the midinfrared band is identified with transitions from the localized states on Cu to the extended states above the Fermi level.

Local density and gradient-corrected functionals for short-range correlation: Antiparallel-spin and non-RPA contributions

Abstract: In many situations, the most long-ranged parts of the exchange and correlation holes surrounding an electron cancel one another. Apparently for this reason, local spin density and generalized gradient approximations are more accurate for exchange and correlation together than for either alone. A study is made of the ability of these density functionals, and also the unmodified second-order gradient expansion, to describe various short-range effects in atoms: the correlation contribution to the interacting kinetic energy, the antiparallel-spin correlation energy, and the correction to the random phase approximation. Generalized gradient approximations, constructed with no adjustable parameter from the electron gas of slowly varying density, are found to give results of useful accuracy for real atoms. Prospects are discussed for use of the new functionals to improve the accuracy of electronic-structure calculations. © 1993 John Wiley & Sons, Inc.

M1 spin strength distribution in 154Sm

Abstract: The effect of the residual spin-spin interaction on the M1 spin-flip strength distribution in 154Sm is studied within the quasi-particle random phase approximation. The double-peaked structure found experimentally is reproduced. A new interpretation for the origin of the two peaks emerges from an analysis of the results. The authors identify these peaks as isoscalar and isovector and discuss previous theoretical interpretations.

Compressible phase of a double-layer electron system with total Landau-level filling factor 1/2.

Abstract: Following recent work of Halperin, Lee, and Read, and Kalmeyer and Zhang, a double-layer electron system with total Landau-level filling factor \ensuremath{ u}=1/2 is mapped onto an equivalent system of fermions in zero average magnetic field interacting via a Chern-Simons gauge field. Within the random-phase approximation a new, low-lying, diffusive mode, not present in the \ensuremath{ u}=1/2 single-layer system, is found. This mode leads to more singular low-energy scattering than appears in the single-layer system, and to an attractive pairing interaction between fermions in different layers which grows stronger as the layer spacing is decreased. The possible connection between this pairing interaction and the experimentally observed fractional quantum Hall effect in double-layer systems is discussed.

Dynamics of multicomponent polymer mixtures via the random phase approximation including hydrodynamic interactions

Abstract: A new and extended formulation of the random phase approximation (RPA) in the study of statics and dynamics of multicomponent polymer mixtures is presented. The new formulation simplifies the implementation of the RPA in both compressible and incompressible mixtures and allows the inclusion of hydrodynamic interaction in the dynamics of polymer melts in the RPA. The dynamics of copolymer melts with hydrodynamic interaction is studied in detail as an illustration of the extended formulation, and the variation of the first cumulant as a function of the wavenumber and interaction parameter is obtained. In this paper we present a generalization of the above elimination procedure by allowing the monomers of the matrix component to interact or to be connected with the monomers in other components, so that the assumption xjo(q,s) = 0, for j = 1, ..., n is no longer needed. This generalization not only simplifies the implementation of the RPA in incompressible multicomponent mixtures in which none of the components consists of homopolymers, such as in melts of copolymers, stars, etc., but also it allows more flexibility in the choice of the bare system in the implementation of the RPA, even in the case of ho-

Many-body treatment of hot-electron scattering from quasiequilibrium electron-hole plasmas and coupled plasmon-longitudinal-optic-phonon modes in GaAs.

Abstract: The interaction of hot electrons (200-300 meV) with neutral electron-hole plasmas in bulk GaAs is theoretically investigated over a range of plasma temperatures and densities. Results obtained using a self-consistent, three-band (electron, heavy-, and light-hole) random-phase approximation for the system's dielectric function, including the lattice susceptibility, are compared with simpler approximations for treating the screened interaction between the hot electrons and the coupled plasma-longitudinal-optic-phonon system. Emphasis is placed on estimating the relative importance of hot-electron plasma versus hot-electron-LO-phonon scattering rates, to the extent that these can be distinguished

Dynamic and static correlations in model Coulomb systems

Abstract: The classical method of moments is applied to express the dynamic structure factor of model two-component plasmas in terms of static correlations. The latter are studied using an original algorithm based on the temperature-Green's-function method and including the local-field corrections to the random-phase approximation

Ionic structure effects on the optical response of lithium clusters

Abstract: The optical response of alkali metal clusters is shown to be sensitive to a proper treatment of the electronion interaction and to the ionic spatial structure. A spherical symmetry model based on a combination of a geometrical optimization of the ionic structure and the random phase approximation (RPA) with exact exchange is applied to calculate the optical response of Li 139 + . The optical response obtained within this model is in good agreement with the measured giant dipole resonance.

Density bistability in an interacting electron-hole system in coherently excited semiconductors.

Abstract: An electron-hole system in a direct-gap semiconductor that is coherently excited by a high-intensity laser is investigated. The stationary state of the system in the presence of laser field is described by Bogolyubov quasiparticles. Using a mean-field approximation, we derive a set of basic equations including electron-electron, hole-hole, and electron-hole screened Coulomb interactions. The screening effects are incorporated self-consistently on the basis of a quasistatic random-phase approximation. The stationary state has a fixed chemical potential and is controlled by the frequency of the laser field