We calculate the resistivity associated with an Ising-nematic quantum critical point in the presence of disorder and acoustic phonons in the lattice model. We use the memory-matrix transport theory, which has a crucial advantage compared to other methods of not relying on the existence of well-defined quasiparticles in the low-energy effective theory. As a result, we obtain that by including an inevitable interaction between the nematic fluctuations and the elastic degrees of freedom of the lattice (parametrized by the nemato-elastic coupling $\kappa_{\text{latt}}$), the resistivity $\rho(T)$ of the system as a function of temperature obeys a universal scaling form described by $\rho(T)\sim T\ln (1/T)$ at high temperatures, reminiscent of the paradigmatic strange metal regime observed in many strongly correlated compounds. For a window of temperatures comparable with $\kappa^{3/2}_{\text{latt}}\varepsilon_F$ (where $\varepsilon_F$ is the Fermi energy of the microscopic model), the system displays another regime in which the resistivity is consistent with a description in terms of $\rho(T)\sim T^{\alpha}$, where the effective exponent roughly satisfies the inequality $1\lesssim\alpha\lesssim 2$. However, in the low-temperature limit (\textit{i.e.}, $T\ll\kappa^{3/2}_{\text{latt}}\varepsilon_F$), the properties of the quantum critical state change in an important way depending on the type of disorder present in the system: It can either recover a conventional Fermi liquid described by $\rho(T)\sim T^2$ or it could exhibit yet another non-Fermi liquid regime characterized by the scaling form $\rho(T)-\rho_0\sim T^2\ln T$. Our results emphasize the key role played by both phonon and disorder effects in the scenario of nematic quantum criticality and might be fundamental for addressing recent transport experiments in some iron-based superconductors.

中文翻译：

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向列量子临界点附近的直流电阻率：弱无序和声学声子的影响

我们计算了在晶格模型中存在无序和声学声子的情况下与伊辛向列量子临界点相关的电阻率。我们使用记忆矩阵传输理论，与其他不依赖低能量有效理论中定义明确的准粒子存在的方法相比，它具有至关重要的优势。因此，我们通过包括向列波动和晶格弹性自由度（由向列弹性耦合 $\kappa_{\text{latt}}$ 参数化）之间不可避免的相互作用，得到电阻率 $\作为温度函数的系统的 rho(T)$ 服从由 $\rho(T)\sim T\ln (1/T)$ 在高温下描述的通用标度形式，让人想起在许多强相关的化合物。对于与 $\kappa^{3/2}_{\text{latt}}\varepsilon_F$（其中 $\varepsilon_F$ 是微观模型的费米能量）相当的温度窗口，系统显示了另一种状态，其中电阻率与 $\rho(T)\sim T^{\alpha}$ 的描述一致，其中有效指数大致满足不等式 $1\lesssim\alpha\lesssim 2$。然而，在低温极限 (\textit{ie}, $T\ll\kappa^{3/2}_{\text{latt}}\varepsilon_F$) 下，量子临界状态的性质在取决于系统中存在的无序类型的重要方式：它可以恢复由 $\rho(T)\sim T^2$ 描述的常规费米液体，或者它可以表现出另一种以缩放为特征的非费米液体状态形式 $\rho(T)-\rho_0\sim T^2\ln T$。