STATIC AND DYNAMIC PROPERTIES OF DOPED HUBBARD CLUSTERS

We study the t-J and the Hubbard models at zero temperature using exact-diagonalization techniques on square-root 10 X square-root 10 and 4 X 4 sites clusters. Quantum Monte Carlo simulation results on larger lattices are also presented. All electronic fillings have been analyzed for the three models. We have measured equal-time correlation functions corresponding to various types of order (ranging from "standard" staggered spin order to more "exotic" possibilities like chiral order), as well as various dynamical properties of these models. Upper bounds for the critical hole doping (x(c)), where long-range antiferromagnetic order disappears, are presented. It was found that x(c) is very small in agreement with experiments for the high- T(c) superconductors. For example, in the t-J model, x(c) < 0.08 at J/t = 0.4. However, short-distance spin correlations are important up to much higher dopings producing a sharp well-defined spin-wave-like peak in S(q = (pi, pi),omega). Regarding the possibility of phase separation in the Hubbard model, we have studied the behavior of the density of particles, [n], as a function of the chemical potential, using the Lanczos method on a 4 X 4 Hubbard cluster, finding no indications of phase separation for any value of U/t. Then, we conclude that the t-J model at small J/t should not phase separate. In order to compare theoretical predictions with photoemission experiments, we evaluated the electronic density of states, N(omega), of the Hubbard and t-J models at several doping fractions. We found that upon doping the antiferromagnetic gap is filled for U approximately 8t or smaller. The chemical potential moves across the insulating gap as one goes from electron to hole doping of the half-filled cluster, in agreement with x-ray absorption experiments but at variance with photoemission experiments. We have also calculated the optical conductivity, sigma-1(omega), of the Hubbard and t-J models at all dopings on 4 X 4 clusters. Results are compared with experiments and the weight of the Drude peak is presented as a function of couplings and dopings. Spectral weight found at small frequencies is associated with the mid-infrared band observed experimentally in La2-xSrxCUO4, and with the states filling the insulating gap in photoemission experiments. An overall good agreement with experiments in the normal state was found. Regarding the possibility of superconductivity in these models, we have studied s-, d-, and p-wave pairing correlations. Naively, the d-wave channel seems enhanced near half filling while the extended s-wave channel seems enhanced from half filling up to 40% doping. However, we found that the enhancement comes from short-distance effects and, thus, no numerical indications of superconductivity were found in these models. We emphasize the importance of analyzing the pairing correlations as a function of distance to distinguish between short- and long-distance effects in the susceptibilities. We also observed that spiral order is enhanced at small J/t and low doping. Uniform chiral order is suppressed by dynamical holes while staggered chiral order may be enhanced, although with a small plaquette order parameter. We conclude with the observation that the simple one-band Hubbard model with intermediate values of U approximately 8t may account for many of the "anomalous" properties of the normal state of the high-T(c) superconductors.