Local dynamics and strong correlation physics: One- and two-dimensional half-filled Hubbard models

We report on a nonperturbative approach to the one-dimensional (1D) and two-dimensional (2D) Hubbard models that is capable of recovering both strong- (U>>t) and weak-coupling (U<0 as would be expected for antiferromagnetic order. We also find that the double occupancy is a smooth monotonic function of U and approaches the anticipated noninteracting limit of 1/4 as U-->0 and vanishes as U-->infinity. Finally, we compute the heat capacity [C(T, U)] for both 1D and 2D. Our results for 1D at moderate to high temperatures are in quantitative agreement with those of the exact Bethe ansatz solution, differing by no more than 1 %. In addition, we find that in 2D, the C(T, U) curves vs T for different values of U exhibit a universal crossing point at two characteristic temperatures T approximate to1.7t+/-0.1t and T approximate to0.4+/-0.1t as is seen universally in Hubbard models and experimentally in a wide range of strongly correlated systems such as He-3, UBe3, and CeCu6-xAlx. The success of this method in recovering well-established results that stem fundamentally from the Coulomb interaction suggests that local dynamics are at the heart of the physics of strongly correlated systems.