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Journal of Physics Condensed Matter

Spin-polarized one-dimensional electron gas with short-range interaction: analytical results

Alfred Gold

Published May 11, 1998• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/10/18/006

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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.
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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.
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Based on its known exact properties and a new set of extensive fixed-node reptation quantum Monte Carlo simulations (both with and without backflow correlations, which in this case turn out to yield negligible improvements), we propose an analytical representation of (i) the spin-summed pair-distribution function and (ii) the spin-resolved potential energy of the ideal two-dimensional interacting electron gas for a wide range of electron densities and spin polarization, plus (iii) the spin-resolved pair-distribution function of the unpolarized gas. These formulas provide an accurate reference for quantities previously not available in analytic form, and may be relevant to semiconductor heterostructures and quantum dots both directly, in terms of phase diagram and spin susceptibility, and indirectly, as key ingredients for the construction of new two-dimensional spin density functionals, beyond the local approximation.