  Using determinant quantum Monte Carlo (DQMC) simulations, we systematically
study the doping dependence of the crossover from one to two dimensions and its
impact on the magnetic properties of the Hubbard model. A square lattice of
chains is used, in which the dimensionality can be tuned by varying the
interchain coupling $t_\perp$. The dynamical spin structure factor and static
quantities, such as the static spin susceptibility and nearest-neighbor spin
correlation function, are characterized in the one- and two-dimensional limits
as a benchmark. When the dimensionality is tuned between these limits, the
magnetic properties, while evolving smoothly from one to two dimensions,
drastically change regardless of the doping level. This suggests that the spin
excitations in the two-dimensional Hubbard model, even in the heavily doped
case, cannot be explained using the spinon picture known from one dimension.
The DQMC calculations are complemented by cluster perturbation theory studies
to form a more complete picture of how the crossover occurs as a function of
doping and how doped holes impact magnetic order.
