Ab initio self-consistent many-body theory of polarons at all couplings

We present a theoretical framework to describe polarons from first principles within a many-body Green's function formalism. Starting from a general electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in which the phonon-mediated self-energy is composed by two distinct terms. One term is the Fan-Migdal self-energy and describes dynamic electron-phonon processes, the other term is a contribution to the self-energy originating from the static displacements of the atomic nuclei in the polaronic ground state. The lowest-order approximation to the present theory yields the standard many-body perturbation theory approach to electron-phonon interactions in the limit of large polarons, and the ab initio polaron equations introduced [Sio et al., Phys. Rev. B 99, 235139 (2019); Phys. Rev. Lett. 122, 246403 (2019)] in the limit of small polarons. A practical recipe to implement the present unifying formalism in first-principles calculations is outlined. We apply our method to the Frohlich model, and obtain remarkably accurate polaron energies at all couplings, in line with Feynman's polaron theory and diagrammatic Monte Carlo calculations. We also recover the well-known results of Frohlich and Pekar at weak and strong coupling, respectively. The present approach enables predictive many-body calculations of polarons in real materials at all couplings.

我们提出了一个理论框架，在多体格林函数形式体系内从第一性原理描述极化子。从一个一般的电子 - 声子哈密顿量出发，我们推导出一个自洽的戴森方程，其中声子介导的自能由两个不同的项组成。一项是范 - 米格达尔自能，描述动态电子 - 声子过程，另一项是对自能的贡献，源于极化子基态中原子核的静态位移。本理论的最低阶近似在大极化子极限下产生电子 - 声子相互作用的标准多体微扰理论方法，以及在小极化子极限下引入的从头算极化子方程[Sio等人，《物理评论B》99，235139（2019年）；《物理评论快报》122，246403（2019年）]。概述了在第一性原理计算中实现这种统一形式体系的实用方法。我们将我们的方法应用于弗罗里希模型，并在所有耦合情况下获得了非常精确的极化子能量，这与费曼的极化子理论和图解蒙特卡罗计算相符。我们还分别在弱耦合和强耦合情况下恢复了弗罗里希和佩卡尔的著名结果。本方法能够对实际材料中在所有耦合情况下的极化子进行预测性的多体计算。