In a wide variety of correlated models, it has been demonstrated that the optical conductivity is significantly influenced by π-ton vertex corrections [1]. These vertex corrections elucidate the coupling between light and bosonic fluctuations associated with a wave vector close to q = (π, π...). While the random phase approximation (RPA) theory of the π-ton vertex corrections [2] in two-dimensional (2D) metallic systems shows that they generally lead to a renormalization of a Drude peak, it has been pointed out in [3] and [4] that in one-dimensional (1D) systems the RPA treatment of π-ton vertex corrections might give rise to a new quasiparticle pole. Therefore, in this work, we semi-analytically study π-ton vertex corrections analogous to the approach in [2], avoiding the use of analytic continuation, to differentiate and identify their characteristic features in correlated metallic systems. Our results suggest that the π-ton vertex corrections to optical conductivity generally tend to suppress the value of the DC conductivity in both 1D and 2D cases. The suppression seems to get stronger as the phase transition is approached and we associated it with the ever-growing correlation length of the critical fluctuations, finally resulting in the displaced Drude peak profile of the optical conductivity. 

 

[1] A. Kauch et al., Phys. Rev. Lett. 124, 047401 (2020).

[2] P. Worm et al., Phys. Rev. B 104, 115153 (2021).

[3] O. Simard et al., Phys. Rev. B 104, 245127 (2021).

[4] O. Simard et al., Phys. Rev. B 103, 104415 (2021).