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.
For nearly a decade, quasi-one-dimensional conductors have been the subject of intensive study. Theoretically, much attention has been devoted to the development of one-dimensional Fermi gas models, some which may be solved exactly, and to the calculation of their response functions. After a review of this theory, a different approach is adopted in the investigation of two models. The dielectric response theory of the three-dimensional Coulomb gas has been applied to an anisotropic system in which the particles interact with an effective one-dimensional long-range potential. Within the framework of the approximation of Singwi, Tosi, Land, and Sjolander, the dielectric properties of the model are examined in order to determine the conditions under which it is unstable with respect to formation of a charge density wave state. It is found that the positive neutralizing background must be polarizable in order for such an instability to occur. The same approximation method, when applied to a one-dimensional fermion gas with a ʃ-function interaction may be compared with the exact solution of Yang. This solution, which exists in the form of coupled integral equations, has been calculated numerically, and, as predicted by the Lieb-Mattis theorem, the ground state is found to be non-magnetic. The approximation of Singwi et al. proves to give better correlation energies than other inexact methods, particularly at higher densities.
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.
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.
We study the one-dimensional electron gas with parabolic dispersion and a repulsive delta-function interaction potential. Using the ladder theory we obtain analytical results for the ground-state energy and the compressibility which are in agreement with exact results for weak and strong coupling. We calculate the short- and the long-distance behaviour of the pair-correlation function g(z) and derive critical exponents from . We evaluate the connection between the local-field correction and critical exponents.
The dielectric response of a quasi-one-dimensional system of interacting electrons has been investigated. In the authors' model the particles move freely in one direction and are tightly bound in the transverse direction. Calculation of the Coulomb matrix elements leads to an effective one-dimensional electron-electron interaction nu (q) which is less singular for small q than the 1/q 2 potential assumed by previous authors. As a result, the excitonic instability which they find even for a rigid positive background does not arise in their calculation. The calculations are based on the approximation of Singwi, Tosi, Land and Sjolander (1968). As expected in this approach, the pair correlation function at small distances remains positive over a much larger range of densities than that for which the compressibility sum rule is satisfied. The static dielectric function is negative around q=2k F , which suggests the possibility of charge ordering when the background is allowed to be polarisable. If nu (q) is replaced by a delta -function potential, a numerical calculation of the energy for the exact solution of Yang may be made. On comparison with the result obtained with the method of Singwi et al. it is found that the approximate scheme gives good correlation energies for high densities.