Doping dependence of the internal energy, spin-density-wave order parameter, and the chemical potential for the Hubbard model.

Abstract

We have applied mean-field theory to calculate the spin-density-wave (SDW) order parameter \ensuremath{\Delta}, the chemical potential \ensuremath{\mu}, and the ground-state energy at various band fillings for the Hubbard model. We have found that at zero temperature and in the large-U limit, the SDW order parameter and the ground-state energy can be written as \ensuremath{\Delta}=U(1-x)/2-O(J) and ${\mathit{E}}_{\mathit{g}}$=-U(1-x${)}^{2}$/4-0(J). The chemical potential obtained here for x=0 and 1 agrees well with the result obtained by the exact-diagonalization calculation on a 4\ifmmode\times\else\texttimes\fi{}4 sites cluster by Dagotto et al. [Phys. Rev. B 45, 10 741 (1992)]. In the SDW phase, the mean-field theory gives an upward shift in the chemical potential as one dopes away from half-filling, which is in contrast with the exact-diagonalization calculations. This result indicates that the Mott-Hubbard gap is depressed much more rapidly in the mean-field theory than the exact-diagonalization calculation. The doping dependence of ground-state energy calculated here is in good agreement with the above numerical calculation for doping up to 0.5. Here, U is the intrasite Coulomb repulsion, x is doping concentration, J=4${\mathit{t}}^{2}$/U is the superexchange interaction parameter, and t is the hopping integral for the nearest neighbors.