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We study the frequency and temperature dependence of the optical conductivityin the weakly coupled two-dimensional Hubbard model using a renormalizedperturbative expansion. The perturbative expansion is based on the skeletonseries for the current-current correlation function with a dressed Green`sfunction and the results are obtained directly on the real frequency axis usingAlgorithmic Matsubara Integration (AMI). The resulting conductivity shows atemperature-independent power law behaviour in the intermediate frequencyregime. Moreover, the associated transport scattering time and renormalizedmass exhibit a Planckian behaviour. We show that the self-energy of the Hubbardmodel, however, is distinct from existing Planckian models. The Planckianbehaviour of the conductivity, observed in optimally doped cuprates forexample, can thus be obtained from a different form of self-energy than thePlanckian model, such as the weakly coupled Hubbard model at half-filling.

Planckian behaviour in the optical conductivity of the weakly coupled Hubbard model