Linear-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> resistivity from spatially random vector coupling

Recently, Patel et al. Science 381, 790 (2023) introduced a higher-dimensional version of the SYK model with random coupling in a Yukawa interaction to explain the linear-$T$ resistivity. We test the universality of this mechanism by replacing the scalar field with a vector field in various dimensions. We find that it applies to vector and scalar interactions, although the details differ significantly. However, this mechanism for 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 role of spatial random disorder and provide a simple explanation of how such random scattering transforms a Fermi liquid into a strange metal by modifying the self-energies of the involved bosons and fermions.