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

TL;DR

This work classifies SYK-rised scalar couplings of the form $(\psi^\dagger\psi)^n\phi^m$ across dimensions to identify candidates for linear-$T$ resistivity in strange metals. Using a G-Σ large-$N$ framework and replica averaging, the authors derive self-consistent Schwinger-Dyson equations for generic $(n,m)$ and analyze the scaling of fermionic and bosonic self-energies, revealing two possible scaling branches and a unique linear regime. They compute the conductivity via the Kubo formula, showing that vertex corrections vanish due to spatial locality, and that linear resistivity is realized only for the 2D Yukawa case ($n=m=1$) with $d=2$, while all other scalar couplings fail to produce linear transport. The results underscore a unique scalar building block for linear-$T$ resistivity in two dimensions and, together with previous vector-coupling work, point toward minimal ingredients required to model strange-metal transport in SYK-rised frameworks.

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 $(ψ^{\dagger}ψ)^nφ^m$ 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.

Figures (2)

• Figure 1: Two self-energies, $\Pi$ and $\Sigma$, share the same structure.
• Figure 2: Polarisation diagrams. The solid line represents the "bare" propagator \ref{['eqn:g1st']}.