Strange metallicity in the Momentum-mixing Hatsugai–Kohmoto model

We study the current response of the Hatsugai–Kohmoto (HK) model and its momentum-mixing extension (MMHK) using Kubo's linear response formalism. At the optical limit q=0, the HK-type interaction does not contribute additional terms to the current operator. For the half-filled HK model, the optical conductivity consists solely of a Drude peak, which vanishes at the Mott transition. Upon doping, owing to the absence of momentum scattering, the DC resistivity scales as T^2 at low temperatures from thermal broadening independent of dimension. Incorporating momentum mixing in the MMHK model restores scattering and yields a robust strange-metal regime: the DC resistivity becomes linear in temperature, persisting to progressively lower temperatures as the number of mixed momenta increases. These results indicate that strange-metal behavior arises naturally from momentum scattering intrinsic to correlated Hubbard-type interactions.