A CDMFT study of antiferromagnetic transition in the square-lattice Hubbard model: optical conductivity and electronic structure

TL;DR

This study uses cluster dynamical mean field theory to analyze how vertex corrections influence optical conductivity and electronic structure near the antiferromagnetic transition in the square-lattice Hubbard model, revealing significant effects on conductivity behavior.

Contribution

It reformulates and applies vertex corrections within CDMFT to study optical conductivity in the antiferromagnetic phase, highlighting their impact on electronic properties.

Findings

Vertex corrections significantly alter conductivity dependencies on temperature and frequency.

Vertex corrections sharpen the Drude and incoherent peaks in conductivity.

The study identifies a temperature region with insulating dc conductivity but metallic optical response.

Abstract

We numerically study optical conductivity $\sigma (\omega )$ near the "antiferromagnetic" phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections, and to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature- and $\omega$-dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the $\omega$-dependence, and sharpen the Drude peak and a high-$\omega$ incoherent peak in the paramagnetic phase. They also enhance the dip in $\sigma (\omega )$ at $\omega$=0 in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but $\sigma (\omega )$ retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.