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

TL;DR

This paper employs a novel RG approach with $k_{||}$ dependence to analyze a ladder system's phase diagram, revealing the significant influence of $k_{||}$ on instabilities and phases such as antiferromagnetism and superconductivity.

Contribution

Introduces an original method to include $k_{||}$ dependence in RG calculations for ladder systems, improving understanding of phase behavior and instabilities.

Findings

Large antiferromagnetic fluctuations near small $t_ot$

Superconducting region with divergence of Spin Density Waves

Suppression of singlet superconductivity and SDWs by non-local backward scattering

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.