SO(5) symmetric ladder

We construct an SO(5) symmetric electron model on a two-chain ladder with purely local interactions on a rung. The ground state phase diagram of this model is determined in the strong-coupling limit. The relationship between the spin-gap magnon mode of the spin-gap insulator and the $\pi$ resonance mode of the $d$-wave pairing phase is discussed. We also present the exact ground state for an SO(5) superspin model.