Mean Field Analysis of the CuO2 Lattice: Comparison to Monte Carlo Simulations
The 2D multi-band Hubbard models have been attracting much attention recently since they provide one of the simplest models for the high Tc superconductors where one assumes the relevant motion is confined to the Cu-O planes. Recent Monte Carlo (MC) studies1,2, using the three-band Hubbard model to describe this motion, have been done in a wide parameter range for various values of doping δ away from half-filling (δ = 0 is defined as one hole per Cu site). We summarize their results as follows: We define the on-site O energy, εp, and the Cu on-site energy, εd. Then there are two basic regimes depending on whether the on-site energy difference e between the O and Cu sites (ε = εp - εd) is greater or less than the onsite Cu Coulomb repulsion Udd. If Udd ≫ ε the behavior of the system is controlled by ε (charge transfer limit). In this case, at half-filling, they find strong antiferrromagnetic correlations and evidence of a charge transfer gap (≈ ε). The antiferromagnetic correlations decrease rapidly as one dopes away from half-filling. In the other case ε ≫ Udd the behavior is controlled by Udd. Here the O occupation is always small and we essentially have an effective single band model with a Mott-Hubbard gap which depends on Udd.
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