We calculate the ground-state energy of a quasi-one-dimensional electron gas with Coulomb interaction depending on the spin-polarization parameter and the Wigner-Seitz parameter . Cylindrical quantum wires of radius are considered. We describe the pair-correlation function g(z = 0) as a function of and . We derive the spin-susceptibility as a function of and in different approximations. Numerical results obtained for the spin-susceptibility are fitted by an analytical expression. Collective modes (charge-density and spin-density excitations) in cylindrical quantum wires are described and the validity range of our calculation is discussed.
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 study the ground state properties of a quasi-one-dimensional electron gas interacting via an effective potential with a harmonic transversal confinement and long-range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows one to sample the exact ground state of the system, even in the low-density regime when the exchange between electrons is extremely small. For different values of the width parameter
b $(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.
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 ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths
b and density parameters
rs. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density. It is observed that the peak in the static structure factor at
k=2kF grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter ${K}_{\ensuremath{\rho}}$ from the momentum density. It is found that ${K}_{\ensuremath{\rho}}$ increases by about 10% between wire widths
b=0.01 and
b=0.5. We also obtain ground-state properties of finite-thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for $b\ensuremath{\ll}{r}_{\text{s}}<1$. It is found that the correlation energy varies as
b2 for $b\ensuremath{\ll}{r}_{\text{s}}$ from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of
b and ${r}_{\text{s}}\ensuremath{\le}1$. These are compared with the QMC results in the range of applicability of the theory.