Optical and DC conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point, including vertex corrections

TL;DR

This study investigates the optical and DC conductivity of the 2D Hubbard model near the pseudogap regime and antiferromagnetic quantum critical point, emphasizing the importance of vertex corrections for accurate results.

Contribution

It introduces a non-perturbative, numerically advanced approach that includes vertex corrections satisfying key physical constraints, revealing their significant impact on conductivity in the pseudogap regime.

Findings

Vertex corrections cause resistivity to decrease in the pseudogap regime.

Resistivity saturates at the Ioffe-Regel limit at high temperatures.

Optical conductivity shows a mid-infrared hump due to antiferromagnetic fluctuations.

Abstract

The conductivity of the two-dimensional Hubbard model is particularly relevant for high-temperature superconductors. Vertex corrections are expected to be important because of strongly momentum dependent self-energies. We use the Two-Particle Self-Consistent approach that satisfies crucial constraints such as the Mermin-Wagner theorem, the Pauli principle and sum rules in order to reach non-perturbative regimes. This approach is reliable from weak to intermediate coupling. A functional derivative approach ensures that vertex corrections are included in a way that satisfies the f sum-rule. The two types of vertex corrections that we find are the antiferromagnetic analogs of the Maki-Thompson and Aslamasov-Larkin contributions of superconducting fluctuations to the conductivity but, contrary to the latter, they include non-perturbative effects. The resulting analytical expressions must be evaluated numerically. The calculations are impossible unless a number of advanced numerical algorithms are used. A maximum entropy approach is specially developed for analytical continuation of our results. The numerical results are for nearest neighbor hoppings. In the pseudogap regime induced by two-dimensional antiferromagnetic fluctuations, the effect of vertex corrections is dramatic. Without vertex corrections the resistivity increases as we enter the pseudogap regime. Adding vertex corrections leads to a drop in resistivity, as observed in some high temperature superconductors. At high temperature, the resistivity saturates at the Ioffe-Regel limit. At the quantum critical point and beyond, the resistivity displays both linear and quadratic temperature dependence and there is a correlation between the linear term and the superconducting transition temperature. A hump is observed in the mid-infrared range of the optical conductivity in the presence of antiferromagnetic fluctuations.