Broadening and sharpening of the Drude peak through antiferromagnetic fluctuations

Antiferromagnetic or charge density wave fluctuations couple with light through the recently discovered {\pi}-ton contribution to optical conductivity, and quite generically constitute dominant vertex corrections in low-dimensional correlated electron systems. Here we study arguably simplest version of these $\pi$-tons based on semi-analytical random phase approximation (RPA) ladder transversal particle-hole channel. The conductivity are calculated directly for real frequencies. We validate that RPA qualitatively reproduces Drude peak Hubbard model. Depending temperature find broaden sharpen peak.