Influence of next-nearest-neighbor electron hopping on the static and dynamical properties of the two-dimensional Hubbard model

Comparing experimental data for high-Tc cuprate superconductors with numerical results for electronic models, it is becoming apparent that a hopping along the plaquette diagonals has to be included to obtain quantitative agreement. However, the values for t^' discussed in the literature were obtained comparing theoretical results in the weak-coupling limit with photoemission data and band-structure calculations. The goal of this paper is to study how t^' gets renormalized as the interaction between electrons, U, increases. For this purpose, the effect of adding a bare diagonal hopping t^' to the two-dimensional Hubbard model Hamiltonian is investigated using numerical techniques. Spin-spin correlations, n(k), 〈n〉 vs {μ}, and local magnetic moments are studied for several values of U/t and the electronic density. The spectral function A(k,{ω}) is also discussed. We introduce a criterion to determine probable locations of Fermi surfaces at zero temperature. In general, we conclude that it is very dangerous to extract a bare parameter of the Hamiltonian (t^') from photoemission spectroscopy data where renormalized parameters play the important role.