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

摘要: The conductivity of the two-dimensional Hubbard model is particularly relevant for high-temperature superconductors. Vertex corrections are expected to be important because strongly momentum-dependent self-energies. To attack this problem, one must also take into account Mermin--Wagner theorem, Pauli principle, and crucial sum rules in order reach nonperturbative regimes. Here, we use two-particle self-consistent approach that satisfies these constraints. This reliable from weak intermediate coupling. A functional derivative ensures vertex included a way $f$-sum rule. two types find antiferromagnetic analogs Maki--Thompson Aslamasov--Larkin contributions superconducting fluctuations but, contrary latter, they include effects. resulting analytical expressions evaluated numerically. calculations impossible unless number advanced numerical algorithms used. These make extensive fast Fourier transforms, cubic splines, asymptotic forms. maximum entropy specially developed continuation our results. explained detail appendices. results nearest-neighbor hoppings. In pseudogap regime induced by fluctuations, effect dramatic. Without resistivity increases as enter regime. Adding leads drop resistivity, observed some At high temperatures, saturates at Ioffe--Regel limit. quantum critical point beyond, displays both linear quadratic temperature dependence there correlation between term transition temperature. hump mid-infrared range optical presence fluctuations.