Localization of overdamped bosonic modes and transport in strange metals

A recent theory described strange metal behavior in a model of a Fermi surface coupled a two-dimensional quantum critical bosonic 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 for wide range of intermediate temperatures, including the linear-in-temperature resistivity. The Harris criterion implies that spatial fluctuations in the local position of the critical point must dominate at low temperatures, and these were not fully accounted for in the recent theory. We use multiple graphics processing units to compute the real frequency spectrum of the boson propagator in a self-consistent mean-field treatment of the boson self-interactions, but an exact treatment of multiple realizations of the spatial randomness from the random boson mass. We find that Landau damping from the fermions leads to behavior consistent with the emergence of the physics of the random transverse-field Ising model, as has been proposed by Hoyos, Kotabage, and Vojta. This emergent low temperature regime, controlled by localized overdamped eigenmodes of the bosonic scalar field, also has a resistivity which is nearly linear-in-temperature, and extends into a `quantum critical phase' away from the quantum critical point, as observed in several cuprates.