Dimensional scaling estimate of the energy of a large system from that of its building blocks: Hubbard model and Fermi liquid
Klaus Capelle, L. Nunes de Oliveira
A simple, physically motivated, scaling hypothesis, which becomes exact in important limits, yields estimates for the ground-state energy of large, composed, systems in terms of the ground-state energy of its building blocks. The concept is illustrated for the electron liquid, and the Hubbard model. By means of this scaling argument the energy of the one-dimensional half-filled Hubbard model is estimated from that of a two-site Hubbard dimer, obtaining quantitative agreement with the exact one-dimensional Bethe-Ansatz solution, and the energies of the two- and three-dimensional half-filled Hubbard models are estimated from the one-dimensional energy, recovering exact results for $U\ensuremath{\rightarrow}0$ and $U\ensuremath{\rightarrow}\ensuremath{\infty}$ and coming close to quantum Monte Carlo data for intermediate $U$.
arXiv:cond-mat/0602333•Physical Review B•Mar 21, 2006•9 citations