Analytical expression for $\pi$-ton vertex contributions to the optical conductivity
Juraj Krsnik, Anna Kauch, Karsten Held
Vertex corrections from the transversal particle-hole channel, so-called \pi π -tons, are gene- ric in models for strongly correlated electron systems and can lead to a displaced Drude peak (DDP). Here, we derive the analytical expression for these \pi π -tons, and how they affect the optical conductivity as a function of correlation length \xi ξ , fermion lifetime \tau τ , temperature T T , and coupling strength to spin or charge fluctuations g g . In particular, for T→ T_c T → T c , the critical temperature for antiferromagnetic or charge ordering, the dc vertex correction is algebraic \sigma_{VERT}^{dc}\propto \xi \sim (T-T_c)^{-\nu} σ V E R T d c ∝ ξ ∼ ( T − T c ) − ν in one dimension and logarithmic \sigma_{VERT}^{dc}\propto \ln\xi \sim \nu \ln (T-T_c) σ V E R T d c ∝ ln ξ ∼ ν ln ( T − T c ) in two dimensions. Here, \nu ν is the critical exponent for the correlation length. If we have the exponential scaling \xi \sim e^{1/T} ξ ∼ e 1 / T of an ideal two-dimensional system, the DDP becomes more pronounced with increasing T T but fades away at low temperatures where only a broadening of the Drude peak remains, as it is observed experimentally, Further, we find the maximum of the DPP to be given by the inverse lifetime: \omega_{DDP
arXiv:2409.11158•SciPost Physics•Apr 25, 2025•0 citations