Correlation of Electrons in a Narrow<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math>Band

TLDR

The approximation’s relation to exact results for one-dimensional models is discussed. The study investigates the ground‑state wave function of electrons in a narrow s band across arbitrary densities and interaction strengths, proposing an approximation that reduces calculations to counting configurations with appropriate weights. The authors compute one‑ and two‑particle density matrices for ferromagnetic and non‑ferromagnetic cases and derive the ground‑state energy assuming only intra‑atomic Coulomb interaction, using the proposed configuration‑counting approximation. Ferromagnetism emerges when the density of states peaks at band edges and the intra‑atomic Coulomb repulsion is strong.

Abstract

The ground-state wave function for the electrons in a narrow $s$ band is investigated for arbitrary density of electrons and arbitrary strength of interaction. An approximation is proposed which limits all the calculations to counting certain types of configurations and attaching the proper weights. The expectation values of the one-particle and two-particle density matrix are computed for the ferromagnetic and for the non-ferromagnetic case. The ground-state energy is obtained under the assumption that only the intra-atomic Coulomb interaction is of importance. Ferromagnetism is found to occur if the density of states is large at the band edges rather than in the center, and if the intra-atomic Coulomb repulsion is sufficiently strong. The relation of this approximation to certain exact results for one-dimensional models is discussed.