A self-consistent, conserving theory of the attractive Hubbard model in two dimensions

TL;DR

This paper develops a self-consistent, conserving theoretical approach to the 2D attractive Hubbard model, revealing non-Fermi liquid behavior without pseudogap formation and highlighting the importance of pair interactions.

Contribution

It introduces a self-consistent, conserving ladder approximation for the 2D attractive Hubbard model, providing new insights into its dynamical and quasiparticle properties.

Findings

No evidence of a pseudogap in the studied parameter region.

Suppression of the Fermi surface does not occur with pair interactions included.

Quasiparticle lifetime varies linearly with temperature, indicating non-Fermi liquid behavior.

Abstract

We have investigated the attractive Hubbard model in the low density limit for the 2D square lattice using the ladder approximation for the vertex function in a self-consistent, conserving formulation. In the parameter region where the on-site attraction is of the order of the bandwidth, we found no evidence of a pseudo gap. Further, we have observed that the suppression of the Fermi surface known to destroy superconductivity in one and two dimensions, when these systems are treated using a non self-consistent theory (Schmitt-Rink, et al., Phys. Rev. Lett. 63, 445 (1989)), does not occur when pair-pair interactions are included. However, we do find a quasiparticle lifetime that varies linearly with temperature, similar to many experiments. Thus, although this system has a Fermi surface, it shows non Fermi liquid type behaviour over a wide temperature range. We stress that our work uses thermal Green's functions along the real time axis, and thus allows for a more accurate determination of the dynamical properties of a model than theories that require extrapolations from the imaginary frequency axis.