Hole motion in the Hubbard model

The motion of a single hole in the half-filled two-dimensional Hubbard model is not fully understood, despite the fact that it constitutes a crucial first step in unravelling the doping evolution of the electronic properties. Here we unambiguously show, using analytical and numerical approaches applied to the various versions of the Hubbard and t-J models, that the hole dynamics is determined by a complex interplay between (i) the strong coupling of a hole to magnons {\it and} (ii) the strongly renormalized, but effectively free, next-nearest neighbor hopping resulting from additional delocalization pathways. By studying the changes in the hole dynamics in the one-to-two-dimensional crossover regime we comment on applicability of the spin-charge separation ansatz and the spin density wave dispersion picture in the single-particle dynamics of the two-dimensional Hubbard model.