Dynamical correlations in the one-dimensional electron gas with short-range interactions

We study the dynamical correlation effects in a one-dimensional Fermion gas with repulsive delta-function interaction within the quantum version of the self-consistent field approximation of Singwi, Tosi, Land, and Sj?lander [Phys. Rev. 176, 589 (1968)]. The dynamic correlation effects are described by a frequency dependent local-field correction . There is a corresponding local-field factor for the spin-density correlations. We investigate the structure factors, spin-dependent pair-correlation functions, the frequency dependences of and , and the plasmon dispersion relation within this formalism. We compare our results with other theoretical approaches, in particular the static version of the self-consistent field approximation to highlight the importance of dynamical correlations. Received 11 December 1998 and Received in final form 25 April 1999     

Many-body properties of a disordered charged Bose gas superlattice

We study some many-body properties of a disordered charged Bose gas (CBG) superlattice—an infinite array of CBG layers each of which containing disorder. The latter is assumed to cause collisions with the charged bosons, the effect of collisions being taken into account through a number-conserving relaxation time approximation incorporated within the random phase approximation (RPA) at T =  0. We go beyond the RPA and include a local-field correction G(q, q_z) which is assumed to be collision independent, as an approximation. The resulting density–density correlation function is then used to calculate a number of many-body quantities of physical interest, e.g. (a) collective modes, (b) static structure factor, (c) energy-loss function, (d) plasmon density of states, and (e) ground-state energy. The effects of collisions on these quantities are discussed, and the results are compared with the corresponding results for an electron gas superlattice.     

Quantum collective field and 1N correction

The collective field method and the large-N limit are applied to go beyond the Hartree-Fock approximation. The correction to the ground-state energy is presented and explicit results are calculated for interacting oscillators and the Bose gas with the δ interaction.     

Spin-polarized electron–electron quantum bilayers: Finite width effect

We study the effect of finite width on the ground-state of a spin-polarized electron–electron quantum bilayers (EEBL) system at temperature T=0. Correlations among carriers are treated beyond the static mean-field theories by using the quantum or dynamical version of Singwi, Tosi, Land and Sjölander (qSTLS) theory. Numerical results are presented for the pair-correlation function, the ground-state energy, the static density susceptibility, and the static local-field correction factor as a function of density parameter r_sl and interlayer spacing d. Interestingly, we find that the inclusion of finite width lowered the critical density, for the onset of Wigner crystal (WC) ground-state, as compared to the similar recent study of spin-polarized EEBL system without finite width effect. Further, spin-polarization effect is seen to introduce a marked change in the ground-state energy of the EEBL system as compared to the results of unpolarized EEBL system with finite width. Results of ground-state energies are also compared with the recent diffusion Monte Carlo (DMC) and variational Monte Carlo (VMC) simulation studies of spin-polarized EEBL system with zero width.     

Instability of layered quantum liquids: 6. Strongly correlated bosons

We calculate the local-field corrections G(q, q _z) for charged bosons at zero temperature in a superlattice with interlayer distance d. An analytical expression for the local-field correction is described. The sum-rule version of the self-consistent approach for the local-field correction is used to discuss the effects of correlation. The RPAparameter r _s and the ratio d/a* determine correlation effects. a* is the effective Bohr radius. The stability region for the Bose condensate r _s < r _sc as a function of d/a* is determined: r _sc ≈ (d/a*)^3/4. The ground-state energy of the layered Bose condensate is calculated and optical and acoustical plasmons are discussed. We predict a roton structure for optical plasmons for r _s > r _sr with r _sr ≈ 0.5 (d/a*)^3/4.     

Magnetpolaron effect in two-dimensional anisotropic parabolic quantum dot in a perpendicular magnetic field

We study the two-dimensional weak-coupling Fr o¨hlich polaron in a completely anisotropic quantum dot in a perpendicular magnetic field. By performing a unitary transformation, we first transform the Hamiltonian into a new one which describes an anisotropic harmonic oscillator with new mass and trapping frequencies interacting with the same phonon bath but with different interaction form and strength. Then employing the second-order Rayleigh–Schr o¨dinger perturbation theory, we obtain the polaron correction to the ground-state energy. The magnetic field and anisotropic effects on the polaron correction to the ground-state energy are discussed.     

Inclusion of the exchange-correlation effects in Ab initio methods for calculating the plasmon dispersion and line width in metals

A self-consistent analog of the Hubbard local-field factor accounting for a real band structure of the metal under investigation is proposed for the calculation of the exchange-correlation corrections to the randomphase approximation. The plasmon energy and the plasmon line width for potassium are calculated as a function of the wave vector. The calculations are performed within the random-phase approximation and with corrections for the local field. It is shown that the results of the calculations are in good agreement with the experimental data. This indicates that, first, the corrections to the random-phase approximation should be taken into account for metals with a low electron density and, second, the local-field factor approximation is an appropriate approach.     

Many-body dipole-induced dipole model for electrorheological fluids

Theoretical investigations on electrorheological (ER) fluids usually rely on computer simulations. An initial approach for these studies would be the point-dipole (PD) approximation, which is known to err considerably when the particles approach and finally touch each other due to many-body and multipolar interactions. Thus various works have attempted to go beyond the PD model. Being beyond the PD model, previous attempts have been restricted to either local-field effects only or multipolar effects only, but not both. For instance, we recently proposed a dipole-induced-dipole (DID) model which is shown to be both more accurate than the PD model and easy to use. This work is necessary because the many-body (local-field) effect is included to put forth the many-body DID model. The results show that the multipolar interactions can indeed be dominant over the dipole interaction, while the local-field effect may yield a correction.     

The local-field correction for the interacting electron gas: many-body effects for unpolarized and polarized electrons

The local-field correction for the three-dimensional and two-dimensional electron gas is calculated within a three-sum-rule version of the self-consistent approach of Singwi, Tosi, Land and Sjölander. Results for 0:01 < r _s < 100 are given and r _s is the RPA-parameter. Correlation effects are studied for the paramagnetic (unpolarized) state and the ferromagnetic (polarized) state and compared with Monte-Carlo calculations and good agreement is found. We conclude that the pair-correlation function and the correlation energy, if calculated within the three-sum-rule approach, shows a better behavior at large rs than if calculated within the two-sum-rule approach. Using the compressibility sumrule we propose a new analytical form of the local-field correction and we compare the dielectric function with recent Monte-Carlo results. We also discuss some new aspects of the one-dimensional electron gas with short-range interaction.     

强耦合简并电子气中离子阻止本领和能量离散的数值计算

利用局域场修正的介电函数,研究了注入离子在强耦合简并电子气中的阻止本领和能量离散。数值结果表明在低速和高r_s值情况下,局域场修正使得阻止本领和能量离散明显地增加。     

Orbital polarization in itinerant magnets

We propose a parameter-free scheme of calculation of the orbital polarization (OP) in metals, which starts with the strong-coupling limit for the screened Coulomb interactions in the random-phase approximation (RPA). For itinerant magnets, RPA can be further improved by restoring the spin polarization of the local-spin-density approximation through the local-field corrections. The OP is then computed as the self-energy correction in the static GW method, which systematically improves the orbital magnetization and the magnetic anisotropy energies in transition-metal and actinide compounds.     

Dynamical exchange corrections to the dielectric function in a two-dimensional electron gas

The effect of dynamical exchange interactions on the dielectric function of a two-dimensional electron gas is studied using a variational approach. Exchange effects are introduced via the local-field correction. The variationally obtained local-field factor is compared to the earlier perturbative result to first order in the electron-electron interaction.     

Dynamical exchange corrections to the dielectric function in a two-dimensional electron gas

The effect of dynamical exchange interactions on the dielectric function of a two-dimensional electron gas is studied using a variational approach. Exchange effects are introduced via the local-field correction. The variationally obtained local-field factor is compared to the earlier perturbative result to first order in the electron-electron interaction.     

Polaron effects on the binding energy of a hydrogenic impurity in parabolic quantum wires in perpendicular electric and magnetic fields

Using a variational approach, the binding energy of shallow hydrogenic impurities in a parabolic quantum wire is calculated within the effective mass approximation. The polaron effects on the ground-state binding energy in electric and magnetic fields are investigated by means of the Pekar–Landau variation technique. The results for the binding energy as well as a polaronic correction are obtained as a function of the applied fields and the impurity positions.     

Theory of the one-dimensional Peierls-Hubbard-model

We consider the properties of a one-dimensional Hamiltonian for electrons and phonons including the Fröhlich electron-phonon interaction as well as the Hubbard term for electron-electron interaction. The unperturbed band structure is of tight-binding form and half-filled.We derive the gap equation and the ground-state energy of the system in mean field approximation.We find antiferromagnetic ordering and lattice distortion and calculate the displacive and magnetic phase limits.D82 (Diss. TH Aachen)     

A correlated-basis-functions approach to realistic nuclear matter

The method of correlated basis functions is adapted to the nuclear-matter problem with two-nucleon potentials containing tensor as well as central components. Procedures are described for evaluating through three-body cluster order the energy expectation value with respect to a constrained trial ground-state wave function incorporating tensor and central correlations, and for calculating in two-body cluster approximation the second-order perturbation correction in a basis of likewise-correlated functions. Results for the 5100, 5200, Gammel-Christian-Thaler and Hamada-Johnston potentials are presented and dissected.     

Electrical conductivity and thermopower of metallic helium

The pair effective interionic interaction, electrical resistance, and thermopower of liquid metallic helium have been calculated over wide temperature and density ranges using the perturbation theory for the potential of electron-ion interaction. For conduction electrons, the random-phase approximation has been used taking into account the exchange interaction and correlations in the local-field approximation. The nuclear subsystem has been described by the hard-sphere model. The sphere diameter is the only parameter of the theory. The diameter and the system density at which helium is transformed from the singly ionized to doubly ionized state have been estimated based on an analysis of the pair effective interaction between helium nuclei. The case of doubly ionized helium atoms has been considered. The numerical calculations have been performed taking into account the perturbation theory in terms up to the third order. In all cases, the role of the third-order correction is significant. In the case of metallic helium, the values of the electrical resistance and its temperature dependence are characteristic of divalent simple liquid metals, as well as the dependences of the thermopower on the density and temperature.     

Influence of Electric and Magnetic Fields on the Polaron in a Quantum Well

A combinative method of variational wavefunction and harmonic oscillator operator algebra, the ground-state energy correction to an electron confined in the quantum well of GaAs/Ga_1-xAl_x, As in the electric and magnetic fields along the growth axis has been studied by taking into account the interaction of different optical phonon modes with the electron. The ground-state energy is obtained as a function of the well width and the strength of electric and magnetic fields. The results show that the magnetic field greatly enhances the in terface-phonon part of the polaronic correction to electron ground-state energy in the well width d ≤ 300 Å. The electric field also enhances the polaron effect of interface mode, but decreases the part of bulk longitudinal mode.     

Ground-state energy of two-dimensional interacting electrons in strong magnetic fields

Summary The ground-state energy of two-dimensional interacting electrons in a strong magnetic field in the angular-momentum representation is studied using a modified Lanczos diagnonalization method. In the presence of a positive background density the ground-state energy increases with the total angular momentum, while a cusp-type behaviour appears. The problem of the electron-impurities interaction is formulated as well. The results are discussed in connection with the observed fractional quantum Hall states. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction. The author of this paper has agreed to not receive the proofs for correction.