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

physical review. b, condensed matter and materials physics

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