Displaced Drude peak from π -ton vertex corrections

Correlated electron systems often show strong bosonic fluctuations, e.g., of antiferromagnetic nature, around a large wave vector such as q=(π,π...). These fluctuations can give rise to vertex corrections to the optical conductivity through the (transversal) particle-hole channel, coined π-ton contributions. Previous numerical results differed qualitatively on how such vertex corrections alter the optical conductivity. Here we clarify that π-ton vertex corrections lead to a displaced Drude peak, by studying the weakly correlated regime of a one-dimensional single-orbital Hubbard model. The proximity and enhancement of the effect when approaching a phase transition of, e.g., antiferromagnetic nature can be utilized for discriminating π-tons in experiments from other physics leading to a displaced Drude peak.