Estimations of the Free Energy for the Hubbard Model

W.‐H. Steeb, E. Marsch

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 $U$.

Minoru Takahashi

W.‐H. Steeb, C. M. Villet

Abstract Two lower bounds for the free energy of the Hubbard model are compared

J. E. Hirsch

François Brouers, Carlos Mauricio Chaves

The authors have derived the free-energy functional of an extended Hubbard model Hamiltonian with interatomic interactions. They have shown that as far as the ferromagnetic transition is concerned universality holds and that introducing a short-range interaction between neighbours yields the same free-energy functional as for the simple Hubbard model if irrelevant terms are discarded.