Renormalization Group calculations with k|| dependent couplings in a ladder

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We calculate the phase diagram of a ladder system, with a Hubbard interaction and an interchain coupling t⊥. We use a Renormalization Group method, in a one loop expansion, introducing an original method to include k|| dependence of couplings. We also classify the order parameters corresponding to ladder instabilities. We obtain different results, depending on whether we include k|| dependence or not. When we do so, 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. We also investigate the effect of a non local 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⊥, of triplet superconductivity. Our results eventually show that k|| is an influential variable in the Renormalization Group flow, for this kind of systems.