Linear-T Resistivity from Spatially Random Vector Coupling

TL;DR

This paper investigates the universality of a mechanism producing linear-T resistivity in higher-dimensional SYK-like models, finding it works only in (2+1) dimensions and explaining how spatial disorder induces strange metal behavior.

Contribution

It demonstrates the dimensional dependence of the linear-T resistivity mechanism and elucidates how spatial randomness transforms Fermi liquids into strange metals.

Findings

Mechanism works for scalar and vector interactions in (2+1) dimensions.

Fails to produce linear-T resistivity in higher dimensions.

Spatial disorder alters self-energies, leading to strange metal behavior.

Abstract

Recently, Patel et al. introduced a higher dimensional version of the SYK model with random coupling in a Yukawa interaction to find the linear-$T$ resistivity. We test the universality of the mechanism by replacing the scalar field with a vector field in various dimensions. We find that it works for vector and scalar interactions, although the details are largely different. However, this mechanism for the 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 r\^ole of spatial random disorder and find a simple explanation of how such random scattering converts the Fermi liquid to a strange metal by changing the self-energies of the involved bosons and fermions.