Monte Carlo results for a two-dimensional Hubbard model in the intermediate-coupling regime U=4t are compared with a diagrammatic spin-fluctuation approximation. Simulations on an 8\ifmmode\times\else\texttimes\fi{}8 lattice doped away from half filling were carried out down to temperatures of order 140 of the bandwidth. Results for the spin susceptibility \ensuremath{\chi}(q,i\ensuremath{\omega}
m), the electron self-energy \ensuremath{\Sigma}(p,i\ensuremath{\omega}
n), various pair-field susceptibilities, and the irreducible particle-particle scattering vertex \ensuremath{\Gamma}(p\ensuremath{'},i\ensuremath{\omega}${}_{\mathrm{n}\ensuremath{'}}$|p,i\ensuremath{\omega}
n) were obtained. A random-phase approximation for \ensuremath{\chi}(q,i\ensuremath{\omega}
m) with a renormalized Coulomb coupling U\ifmmode\bar\else\textasciimacron\fi{} is shown to provide a fit to the Monte Carlo data. A similar approximation for the Berk-Schrieffer spin-fluctuation interaction also provides a reasonable fit to the self-energy \ensuremath{\Sigma}(p,i\ensuremath{\omega}
n) in the region explored by the Monte Carlo data. However, a similar approximation for the irreducible particle-particle interaction failed to reproduce the Monte Carlo results. Higher-order vertex corrections were calculated, but significant discrepancies with Monte Carlo results for \ensuremath{\Gamma} remain.
Dynamic cluster Monte Carlo calculations for the doped two-dimensional Hubbard model are used to study the irreducible particle-particle vertex responsible for dx2-y2 pairing in this model. This vertex increases with increasing momentum transfer and decreases when the energy transfer exceeds a scale associated with the Q=(pi, pi) spin susceptibility. Using an exact decomposition of this vertex into a fully irreducible two-fermion vertex and charge and magnetic exchange channels, the dominant part of the effective pairing interaction is found to come from the magnetic, spin S=1 exchange channel.
Here we discuss Quantum Monte Carlo results for the magnetic susceptibility, single-particle spectral weight and the irreducible particle-particle interaction vertex of the two-dimensional Hubbard model. In the doped system, as the temperature is lowered below J=4t^2/U, short-range antiferromagnetic correlations develop. These lead to a narrow low-energy quasiparticle band with a large Fermi surface and a particle-particle vertex which increases at large momentum transfer, which favor d_{x^2-y^2}-pairing.
We study the spin and charge fluctuations of the extended Hubbard model with on-site interaction
U and first neighbor interaction
V on the two-dimensional square lattice in the weak to intermediate coupling regime. We propose an extension of the two-particle self-consistent approximation that includes the effect of functional derivatives of the pair-correlation functions on irreducible spin and charge vertices. These functional derivatives were ignored in our previous work. We evaluate them assuming particle-hole symmetry. The resulting theory satisfies conservation laws and the Mermin-Wagner theorem. Our current results are in much better agreement with benchmark quantum Monte Carlo results. This theory allows us to reliably determine the crossover temperatures toward renormalized-classical regimes, and hence, the dominant instability as a function of
U and
V. We have considered fillings
n=1 and
n=0.75. Either spin or charge fluctuations can dominate. The wave vector is self-determined by the approach.
We investigate the charge- and spin-dynamical structure factors for the two-dimensional one-band Hubbard model in the strong coupling regime within the dynamical cluster approximation (DCA) that is explicitly extended to two-particle response functions. The full irreducible two-particle vertex with three momenta and frequencies is approximated by an effective vertex dependent on the momentum and frequency of the spin and/or charge excitation. In the spirit of the DCA, the effective vertex is calculated by using the quantum Monte Carlo methods on a finite cluster. On the basis of a comparison to high temperature auxiliary field quantum Monte Carlo data, we show that near and beyond optimal doping, our results provide a consistent overall picture of the interplay between charge, spin, and single-particle excitations.
Particle-hole-magnetic and particle-particle-pairing susceptibilities can be expressed in terms of dressed Green's functions and interaction vertices. Using quantum Monte Carlo simulation techniques, the effect of the interaction vertices is examined to determine the sign and relative magnitude of the effective pairing interaction in various channels for the two-dimensional Hubbard model. Near half filling we find that the singlet ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing interaction is the most attractive. The extended near-neighbor
s interaction is also weakly attractive, while the singlet
sxy and
dxy and the triplet
px interactions are repulsive.