The Wiedemann-Franz (WF) law, stating that the Lorenz ratio L = κ/(Tσ) between the thermal and electrical conductivities in a metal approaches a universal constant \({L}_{0}={\pi }^{2}{k}_{B}^{2}/(3{e}^{2})\) at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids also obey the WF law at T → 0. Instead, we propose using the leading low-temperature correction to the WF law, L(T) − L₀ (proportional to the inelastic scattering rate), to distinguish different types of strange metals. As an example, we demonstrate that in a solvable model of a marginal Fermi-liquid, L(T) − L₀ ∝ − T. Using the quantum Boltzmann equation (QBE) approach, we find analogous behavior in a class of marginal- and non-Fermi liquids with a weakly momentum-dependent inelastic scattering. In contrast, in a Fermi-liquid, L(T) − L₀ is proportional to − T². This holds even when the resistivity grows linearly with T, due to T − linear quasi-elastic scattering (as in the case of electron-phonon scattering at temperatures above the Debye frequency). Finally, by exploiting the QBE approach, we demonstrate that the transverse Lorenz ratio, L_xy = κ_xy/(Tσ_xy), exhibits the same behavior.

维德曼-弗朗茨 (WF) 定律，指出金属的导热系数和导电系数之间的洛伦兹比率L  =  κ /( T σ ) 接近通用常数\({L}_{0}={\pi }^低温下的{2}{k}_{B}^{2}/(3{e}^{2})\)通常被解释为费米子朗道准粒子的特征。相比之下，我们表明弱无序非费米液体的各种模型在T  → 0 时也遵循 WF 定律。相反，我们建议使用 WF 定律的领先低温修正L ( T ) −  L ₀（比例到非弹性散射率），以区分不同类型的奇怪金属。作为一个例子，我们证明了在边际费米液体的可解模型中，L ( T ) −  L ₀  ∝  −  T。使用量子玻尔兹曼方程（QBE）方法，我们在一类具有弱动量依赖性非弹性散射的边际和非费米液体中发现了类似的行为。相反，在费米液体中，L ( T ) -  L _{0与 -} T ²成比例 。即使当电阻率随T线性增长时，由于T  − 线性准弹性散射（如在高于德拜频率的温度下电子声子散射的情况），这一点仍然成立。最后，通过利用 QBE 方法，我们证明横向洛伦兹比L _{x y}  =  κ _{x y} /( T σ _{x y} ) 表现出相同的行为。