Linear-T Resistivity from Spatially Random Vector Coupling

Recently, Patel et al. introduced a higher dimensional version of the SYK model with random coupling in a Yukawa interaction to find the linear-$T$ resistivity. We test the universality of the mechanism by replacing the scalar field with a vector field in various dimensions. We find that it works for vector and scalar interactions, although the details are largely different. However, this mechanism for the linear-$T$ resistivity works only in $(2+1)$ dimensions and not in higher dimensions, regardless of the interaction type. Based on these results, we explore the r\^ole of spatial random disorder and find a simple explanation of how such random scattering converts the Fermi liquid to a strange metal by changing the self-energies of the involved bosons and fermions.