Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase

TL;DR

This paper investigates electronic instabilities in a 2D Hubbard model with finite width, revealing how interactions near Van Hove singularities lead to a breakdown of metallic behavior and the emergence of d-wave superconductivity.

Contribution

It introduces a nonperturbative bosonization and renormalization group approach to analyze the competition between superconductivity and pseudogap phases in a coupled chain Hubbard model.

Findings

Fermi liquid behavior emerges as the number of chains increases.

Van Hove singularities cause divergence of electron dimensions at low energies.

d-wave superconducting correlations grow but are suppressed by fermion excitation gaps.

Abstract

We study the electronic instabilities in a 2D Hubbard model where one of the dimensions has a finite width, so that it can be considered as a large array of coupled chains. The finite transverse size of the system gives rise to a discrete string of Fermi points, with respective electron fields that, due to their mutual interaction, acquire anomalous scaling dimensions depending on the point of the string. Using bosonization methods, we show that the anomalous scaling dimensions vanish when the number of coupled chains goes to infinity, implying the Fermi liquid behavior of a 2D system in that limit. However, when the Fermi level is at the Van Hove singularity arising from the saddle points of the 2D dispersion, backscattering and Cooper-pair scattering lead to the breakdown of the metallic behavior at low energies. These interactions are taken into account through their renormalization group scaling, studying in turn their influence on the nonperturbative bosonization of the model. We show that, at a certain low-energy scale, the anomalous electron dimension diverges at the Fermi points closer to the saddle points of the 2D dispersion. The d-wave superconducting correlations become also large at low energies, but their growth is cut off as the suppression of fermion excitations takes place first, extending progressively along the Fermi points towards the diagonals of the 2D Brillouin zone. We stress that this effect arises from the vanishing of the charge stiffness at the Fermi points, characterizing a critical behavior that is well captured within our nonperturbative approach.