统一处理关联金属中局域动力学相互作用的 Eliashberg 理论方法

中文摘要 AI 辅助

具有强电子关联材料的第一性原理研究引入了额外的理论复杂性和计算成本，如果晶格自由度也起作用，则更是如此。为了应对这些挑战，我们展示了如何一致地处理直接和声子介导的电子-电子相互作用。关键观察是 GW 和 Fan-Migdal 自能是拓扑上相同的图，因此可以使用单一有效相互作用（即两者之和）来统一处理。电子格林函数的 Dyson 方程随后产生正常态 Eliashberg 方程，这可被视为耦合电子和声子的 Hedin-Baym 方程的一个子集 [Phys. Rev. X 13, 031026 (2023)]。我们在局域近似下求解这些动力学方程，以从第一性原理计算温度相关的准粒子谱，并特别关注决定输运的低能窗口。我们将这种扩展的动力学 Hubbard 方法应用于关联金属 Sr$_2$RuO$_4$，该材料长期以来一直是先进电子结构方法的基准系统。由此产生的准粒子带重整化与实验和动力学平均场理论的结果定性一致。然而，在气泡近似的 Green-Kubo 框架内，这里的低能线宽和相应的电阻率被低估，表明需要顶点修正。这项工作强调了简单的动力学表述如何为研究关联材料提供一个可扩展的框架，该框架平等地处理电子和振动激发。

英文摘要

First-principles studies of materials with strong electronic correlations introduce additional theoretical complexities and computational costs, even more so if lattice degrees of freedom also play a role. To address these challenges, we show how direct and phonon-mediated electron-electron interactions can be treated consistently. The key observation is that the GW and Fan-Migdal self-energies are topologically the same diagram, so that they can be unified using a single effective interaction, which is the sum of the two interactions. The Dyson equation for the electron Green function then yields normal-state Eliashberg equations, which can be viewed as a subset of the Hedin-Baym equations for coupled electrons and phonons [Phys. Rev. X 13, 031026 (2023)]. We solve these dynamical equations in a local approximation to calculate from first principles the temperature-dependent quasiparticle spectrum, with close attention to the low-energy window determining transport. We apply this extended dynamical Hubbard approach to the correlated metal Sr$_2$RuO$_4$, which has long served as a benchmark system for advanced electronic-structure methods. The resulting renormalization of quasiparticle bands is in qualitative agreement with experiments and results from dynamical mean-field theory. However, here the low-energy linewidth and associated resistivity within the Green-Kubo formalism in the bubble approximation are underestimated, suggesting the need for vertex corrections. This work highlights how simple dynamical formulations can provide an extensible framework for studying correlated materials, which treats electronic and vibrational excitations on equal footing.

发表机构

• University of Bremen（不来梅大学）
• Université catholique de Louvain（鲁汶天主教大学）
• WEL Research Institute（WEL研究院）
• École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
• University of Cambridge（剑桥大学）
• California Institute of Technology（加州理工学院）

机构由 AI 辅助整理，请以论文原文为准。

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15 pages, 6 figures