Dimensionality effects on the charge gap in the dimerized Hubbard model atquarter filling: The density-matrix and perturbative renormalization-groupapproaches

We study dimensionality effects on the charge gap in the dimerized Hubbard model at quarter filling, with two approaches. First, we examine three chai ns coupled via the interchain one-particle hopping integral t(b), by the de nsity-matrix renormalization-group (DMRG) method. Next, we consider the d = 1 + epsilon dimensional model, using the perturbative renormalization-grou p (PRG) method. The dimensionality is controlled through t(b) and epsilon, respectively. Both approaches lead to the conclusion that, for a finite dim erization ratio, the charge gap decreases as the dimensionality increases.