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 ${t}_{\ensuremath{\perp}}$. We use a renormalization-group method, in a one loop expansion, introducing an original method to include ${k}_{\ensuremath{\Vert}}$ dependence of couplings. We also classify the order parameters corresponding to ladder instabilities. We obtain different results, depending on whether we include ${k}_{\ensuremath{\Vert}}$ dependence or not. When we do so, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small ${t}_{\ensuremath{\perp}}$, 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 ${t}_{\ensuremath{\perp}}$, of triplet superconductivity. Our results eventually show that ${k}_{\ensuremath{\Vert}}$ is an influential variable in the renormalization-group flow, for this kind of system.