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 models and the Hubbard model in single-site dynamical mean-field theory. 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. Thus not only do we 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.”

中文翻译：

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来自局部自能的斜率不变T线电阻率

对神秘的温度线性关系的理论理解（$Ť$在高度相关的金属系统中普遍存在的电阻率一直是人们追求的目标。此外，这种坚固的斜率$Ť$线性电阻率还可以通过在不同温度范围之间的转换而保持恒定：这种现象我们称之为“斜率不变性”。最近，一些可解决的模型$Ť$提出了线性电阻率，使我们有机会在各种显式计算中比较它们的内部工作原理。我们考虑两个具有本地自能量的高度相关的模型$Ť$线性：单点动力平均场理论中耦合的Sachdev-Ye-Kitaev模型和Hubbard模型的晶格。我们发现两个模型实现了$Ť$在中间温度下通过不同的机理获得线性关系。但是，我们还发现，这些机制在高温下会收敛为相同的形式。出乎意料的是，两个模型在两个温度范围内均表现出“斜率不变性”。因此，我们不仅揭示了理论内部运作中的某些多样性，还可能导致$Ť$-线性电阻率，但我们还确定了不同的机制会导致“坡度不变”。