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

Abstract

We calculate the phase diagram of a ladder system, with a Hubbard interaction and an interchain coupling $t_{\perp }$. 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 $t_{\perp }$, 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 $t_{\perp }$, of triplet superconductivity. Our results eventually show that $k_{||}$ is an influential variable in the Renormalization Group flow, for this kind of systems.

20 pages, 19 figures, accepted in Phys. Rev. B 71 v. 24

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