Electronic ladders with SO(5) symmetry: Phase diagrams and correlations at half filling

We construct a family of electronic-ladder models with SO(5) symmetry that have exact ground states in the form of finitely correlated wave functions. Extensions for these models preserving this symmetry are studied using these states in a variational approach. Within this approach, the zero-temperature phase diagram of these electronic ladders at half filling is obtained, reproducing the known results in the weak coupling (band insulator) and strong-coupling regime, first studied by Scalapino, Zhang, and Hanke. Finally, the compact form of the variational wave functions allows us to compute various correlation functions for these systems.