Planckian Bounds via Spectral Moments of Optical Conductivity

Abstract: The observation of Planckian scattering, often inferred from Drude fits in strongly correlated metals, raises the question of how to extract an intrinsic timescale from measurable quantities in a model-independent way. We address this by focusing on a ratio (${\cal{B}}$) of spectral moments of the dissipative part of the optical conductivity and prove a rigorous upper bound on ${\cal{B}}$ in terms of the Planckian rate. The bound emerges from the analytic structure of thermally weighted response functions of the current operator. Crucially, the bounded quantity is directly accessible via optical spectroscopy and computable from imaginary-time correlators in quantum Monte Carlo simulations, without any need for analytic continuation. We evaluate ${\cal{B}}$ for simplified examples of both Drude and non-Drude forms of the optical conductivity with a single scattering rate in various asymptotic regimes, and find that ${\cal{B}}$ lies far below the saturation value. These findings demonstrate that Planckian bounds can arise from fundamental constraints on equilibrium dynamics, pointing toward a possibly universal structure governing transport in correlated quantum matter.