Renormalized SO(5) Symmetry in Ladders with Next-Nearest-Neighbor Hopping

We study the occurrence of SO(5) symmetry in the low-energy sector of two-chain Hubbard-like systems by analyzing the flow of the running couplings ( $g$-ology) under renormalization group in the weak-interaction limit. It is shown that SO(5) is asymptotically restored for low energies for rather general parameters of the bare Hamiltonian. This holds also with the inclusion of a next-nearest-neighbor hopping which explicitly breaks particle-hole symmetry if one accounts for a different single-particle weight for the quasiparticles of the two bands of the system. The physical significance of this renormalization SO(5) symmetry is discussed.