Dimensionality effects on the charge gap in the dimerized Hubbard model at quarter filling: The density-matrix and perturbative renormalization-group approaches

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