Linear Resistivity from Spatially Random Interactions and the Uniqueness of Yukawa Coupling

TL;DR

This paper classifies scalar couplings in disordered systems and finds that only spatially random Yukawa interactions in 2+1 dimensions can produce linear-in-temperature resistivity, characteristic of strange metals.

Contribution

It systematically classifies scalar couplings and identifies the specific conditions under which linear resistivity arises in disordered quantum systems.

Findings

Only spatially random Yukawa interactions in 2+1 dimensions produce linear resistivity.

Scalar couplings of the form $(ar{ abla} abla)^n ightarrow ext{scalar}$ are classified.

The study clarifies the conditions for strange-metal behavior in disordered models.

Abstract

Recent studies have shown that a spatially random Yukawa-type interaction between a Fermi surface and critical bosons can produce linear-in-temperature resistivity, the defining signature of strange metals. In this article, we systematically classify all scalar couplings of the form $(\psi^{\dagger}\psi)^n\phi^m$ in arbitrary dimensions to identify possible candidates for strange-metal behaviour within this disordered framework. We find that only spatially random Yukawa-type interaction in $(2+1)$ dimensions can yield linear resistivity.