PENSON-KOLB-HUBBARD MODEL - A STUDY OF THE COMPETITION BETWEEN SINGLE-PARTICLE AND PAIR HOPPING IN ONE-DIMENSION

In this paper, we present a study of the ground-state phase diagram of a one-d [GRAPHICS] at half filling. We have examined the system using exact diagonalization for samples of up to 12 sites and employed two techniques, eigenprojection decomposition and twisted-boundary conditions, in analyzing the data. These techniques allow us to characterize the ground state in a manner insensitive to changes in sample size and provide us with a clean way to visualize the physics. When used with the ''correct'' order parameter, qualitative features emerge even for sample sizes as small as six sites. We find that the second-order charge-density-wave-spin-density-wave transition in the weak-coupling limit (t >> U is similar to 2V turns into a first-order superconducting-antiferromagnetic transition in the strong-coupling regime [t << U is similar to (4/tau)V]. We also observe evidence of a charge-density-wave-superconducting transition in the parameter range (t is similar to V >> U). These three transition lines meet together at a tricritical point at (t:U:V) is similar to (0.04:0.54:0.42). A naive renormalization-group analysis in the intermediate-coupling regime produces results consistent with this conclusion.