Non-perturbative treatment of charge and spin fluctuations in the two-dimensional extended Hubbard model: Extended two-particle self-consistent approach

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.