ONE-DIMENSIONAL PAIR HOPPING AND ATTRACTIVE HUBBARD MODELS - A COMPARATIVE-STUDY

The low-energy physics of the one-dimensional pair hopping (PH) and at tractive Hubbard models are expected to be similar. Based on numerical calculations on small chains, several authors have recently challenge d this idea and predicted the existence of a phase transition at half filling and finite positive coupling for the pair-hopping model. We re examine the controversy by making systematic comparisons between numer ical results obtained for the PH and attractive Hubbard models. To do so, we have calculated the Luttinger parameters (spin and charge veloc ities, stiffnesses, etc.) of the two models using both the density mat rix renormalization-group method for large systems and Lanczos calcula tions with twisted boundary conditions for smaller systems. Although m ost of our results confirm that both models are very similar we have f ound some important differences in the spin properties for the small s izes considered by previous numerical studies (6-12 sites). However, w e show that these differences disappear at larger sizes (14-42 sites) when sufficiently accurate eigenstates are considered. Accordingly, ou r results strongly suggest that the ground-state phase transition prev iously found for small systems is a finite size artifact. Interpreting our results within the framework of the Luttinger liquid theory, we d iscuss the origin of the apparent contradiction between the prediction s of the perturbative renormalization-group approach and numerical cal culations at small sizes.