Model of a non-Fermi liquid with power-law resistivity: Strange metal with a not-so-strange origin

We construct a model that exhibits resistivity going as a power law in temperature $T$, as $T^{\alpha }$ down to the lowest temperature. There is no residual resistivity because we assume the absence of disorder and momentum relaxation is due to umklapp scattering. Our model consists of a quantum spin liquid state with a spinon Fermi surface and a hole Fermi surface made out of doped holes. The key ingredient is a set of singular $2k_F$ modes living on a ring in momentum space. Depending on parameters, $\alpha$ may be unity (strange metal) or even smaller. The model may be applicable to a doped organic compound, which has been found to exhibit linear $T$ resistivity. We conclude that it is possible to obtain strange metal behavior starting with a model that is not so strange.