We investigate the phase diagram of a ladder system (two chains, with a Hubbard interaction U and an interband coupling t ? ). It is already known [M. Fabrizio, Phys. Rev. B 48 (1993) 15838] that backward interband scattering รฐg b ร plays a particular role in this system. Moreover, some authors (for instance [H.J. Schulz, Phys. Rev. B 53 (1996) R2959]) have early pointed out that, because of this coupling g b , parallel momentum รฐk k ร dependence could not be neglected. So we have introduced an original method to include k k dependence of couplings, in a RG calculation using the one particle irreducible (OPI) scheme.
We calculate different susceptibilities, which are classified according to their symmetries. Our results depend on whether we include k k dependence or not. When we include this dependence, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small t ? , followed by a superconducting region with a simultaneous divergence of the spin density waves channel. The region with only spin density wave fluctuations disappears, when k k dependence is neglected.
Altogether, our results prove that k k is an influential variable in the renormalization group flow, for a ladder.