$T$-linear resistivity in models with local self-energy

TL;DR

This paper compares two strongly correlated models exhibiting linear-in-temperature resistivity, revealing diverse mechanisms behind this behavior and the phenomenon of slope invariance across temperature regimes.

Contribution

It demonstrates that different theoretical mechanisms can produce T-linear resistivity and slope invariance in models with local self-energy, unifying high-temperature behavior.

Findings

Models achieve T-linearity through distinct intermediate-temperature mechanisms.

Both models exhibit slope invariance across temperature regimes.

High-temperature mechanisms converge to an identical form.

Abstract

A theoretical understanding of the enigmatic linear-in-temperature ($T$) resistivity, ubiquitous in strongly correlated metallic systems, has been a long sought-after goal. Furthermore, the slope of this robust $T$-linear resistivity is also observed to stay constant through crossovers between different temperature regimes: a phenomenon we dub "slope invariance". Recently, several solvable models with $T$-linear resistivity have been proposed, putting us in an opportune moment to compare their inner workings in various explicit calculations. We consider two strongly correlated models with local self-energies that demonstrate $T$-linearity: a lattice of coupled Sachdev-Ye-Kitaev (SYK) models and the Hubbard model in single-site dynamical mean-field theory (DMFT). We find that the two models achieve $T$-linearity through distinct mechanisms at intermediate temperatures. However, we also find that these mechanisms converge to an identical form at high temperatures. Surprisingly, both models exhibit "slope invariance" across the two temperature regimes. We thus not only reveal some of the diversity in the theoretical inner workings that can lead to $T$-linear resistivity, but we also establish that different mechanisms can result in "slope invarance".