Renormalization-group calculations with k∥-dependent couplings in a ladder

We calculate the phase diagram of a ladder system, with a Hubbard interaction and an interchain coupling t Ќ. We use a renormalization-group method, in a one loop expansion, introducing an original method to include k ʈ dependence of couplings. We also classify the order parameters corresponding to ladder instabilities. We obtain different results, depending on whether we include k ʈ dependence or not. When we do so, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small t Ќ , followed by a superconducting region with a simultaneous divergence of the spin density waves channel. We also investigate the effect of a nonlocal backward interchain scattering: we observe, on one hand, the suppression of singlet superconductivity and of spin density waves, and, on the other hand, the increase of charge density waves and, for some values of t Ќ , of triplet superconductivity. Our results eventually show that k ʈ is an influential variable in the renormalization-group flow, for this kind of system.