Static and dynamical properties of doped Hubbard clusters

Abstract

We study the t-J and the Hubbard models at zero temperature using exact-diagonalization techniques on √10 × √10 and 4×4 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 (${\mathit{x}}_{\mathit{c}}$), where long-range antiferromagnetic order disappears, are presented. It was found that ${\mathit{x}}_{\mathit{c}}$ is very small in agreement with experiments for the high-${\mathit{T}}_{\mathit{c}}$ superconductors. For example, in the t-J model, ${\mathit{x}}_{\mathit{c}}$<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=(π,π),ω). 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 4×4 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.