Electron-Spin Interaction in High-Tc Superconductors

In this paper, we study numerically the renormalization of the electron-spin (el-sp) interaction or vertex due to Coulomb correlations in a two-dimensional one-band Hubbard model with spin-fluctuation momentum transfer q = (π, π). Our simulations are based on a new numerically exact technique to extract the vertex, which is especially important for the physically relevant case, i.e., strong correlations, which cannot be controlled perturbatively. We find that the renormalized el-sp vertex decreases quite generally with increasing doping from the underdoped to the overdoped region. In the underdoped region, the corresponding effective pairing interaction increases strongly with lowering temperature in the weak- to intermediate-correlation regime. In contrast to this, it depends weakly on temperature in the strong-correlation regime. This behavior in the physically relevant strong-correlation case is due to a near cancellation between the temperature-driven enhancement of the spin susceptibility χ and the reduction of the el-sp interaction vertex. Thus, the spin-mediated d-wave attraction, which is peaked in weak coupling due to χ, is strongly reduced due to the el-sp vertex corrections for strong correlations.