Strong disorder effects in the theory of strange metals

A recent theory has described strange metal behavior in a model of a Fermi surface coupled a two-dimensional quantum-critical scalar field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal were obtained, including the linear-in-temperature resistivity. The Harris criterion implies that the self-averaging of randomness must fail at low enough temperatures near the quantum critical point. We examine the spectrum of the scalar propagator in each random realization, assuming Landau-damping from the fermions, a spatially random mass, and a continuous flavor symmetry. We find behavior consistent with emergence of the physics of the random transverse-field Ising model, as has been proposed earlier by Hoyos, Kotabage, and Vojta. This emergent low temperature regime also has resistivity which is (nearly) linear-in-temperature, and extends into a "foot" away from the quantum-critical fan, as observed in several cuprates.