We discuss interaction effects for the one-dimensional electron gas with a repulsive \ensuremath{\delta}-function interaction potential by using the random-phase approximation and a local-field correction. Analytical results for the local-field correction of charge-density fluctuations and spin-density fluctuations are obtained. The ground-state energy is found to be in better agreement with the exact result than the ground-state energy calculated within the random-phase approximation. We calculate the pair-correlation functions for electrons with parallel and antiparallel spins and the paramagnetic susceptibility. The energies of the collective density modes ${\mathrm{\ensuremath{\omega}}}_{\mathrm{d}}$ (q) and the collective spin modes ${\mathrm{\ensuremath{\omega}}}_{\mathrm{s}}$ (q) are calculated and compared with the energy of the electron-hole excitations ${\mathrm{\ensuremath{\omega}}}_{\mathrm{eh}\ifmmode\pm\else\textpm\fi{}}$ (q): ${\mathrm{\ensuremath{\omega}}}_{\mathrm{d}}$ (q\ensuremath{\rightarrow}0)>${\mathrm{\ensuremath{\omega}}}_{\mathrm{eh}\ifmmode\pm\else\textpm\fi{}}$ (q\ensuremath{\rightarrow}0)>${\mathrm{\ensuremath{\omega}}}_{\mathrm{s}}$ (q\ensuremath{\rightarrow}0). The critical exponents for the long-distance behavior of correlation functions are found to be described by local-field corrections. We compare our results for the critical exponents with recent results obtained by bosonization techniques and the conformal field theory.
We study spin-polarization effects in the one-dimensional electron gas with parabolic dispersion and a repulsive delta-function interaction potential. Using quasi-exact results for the unpolarized system and exact results for the fully polarized system we derive quasi-exact analytical results for the ground-state energy as a function of the spin polarization and the interaction strength. The spin susceptibility as a function of the interaction strength is calculated and compared with other calculations. We present results for the sound velocity of collective spin excitations and the sound velocity of collective density excitations.
We study the correlation effects in a one-dimensional Bose gas with repulsive delta-function interaction. The correlation effects are described by a local-field correction which takes into account the short-range correlations. We find that the ground state energy is in good agreement with the exact result up to intermediate coupling strengths, showing an improvement over the Bogoliubov and other related approximations. The velocity of sound, the static structure factor, and pair-correlation function are also calculated within the present approximation.
We present analytical and numerical results for the pair-correlation function
g(r=0) of the electron gas with long-range Coulomb interaction obtained within the ladder theory. Analytical results obtained by perturbation calculation and a Pad\'e approximation are derived and are found to be in good agreement with our numerical solution of the ladder equation. Finite-width effects in the two-dimensional electron gas (quantum well) are also described. For quasi-one-dimensional systems (quantum wires) numerical and analytical results are derived for an oscillator confinement model.
We have evaluated the density-density response of the two-dimensional electron gas at zero temperature by solving the Dyson equation for the particle-hole Green's function, including exchange Coulomb matrix elements and short-range contributions in the ladder approximation. We study the effect of these correlations on the total energy, compressibility per particle, local field factor G ( q ), static structure factor and pair-correlation function. Results are compared with the normal random-phase approximation, local field theories and quantum Monte Carlo calculations.
In this paper, we study correlations in quasi-one-dimensional electron systems. To account for the short-range correlations we have used a ladder approximation (LA), and to account for the long-range correlations we have used the Singwi, Tosi, S\"olander, and Land (STLS) scheme. After solving the integral equation appearing in the LA and solving the set of self-consistent equations of the STLS scheme, we join the resulting static structure factor in the large- and small-
q limit smoothly. We then calculate the pair-correlation functions, the ground-state energy, the screened potential, and the plasmon dispersion relation. Our pair-correlation function remains positive everywhere (for
rs< 6.5) and its value at the origin,
g(0), is compared with the results of other calculational schemes. The screened potential is repulsive for
rs< 2 and shows a weak attractive part for
rs>2. We have argued that in these systems the
s-wave intrinsic superconductivity is absent. Finally, the quantities calculated in this paper are compared with the results of other calculational schemes.