ファインマン図を用いて実材料の特性を予測（Adding Up Feynman Diagrams to Make Predictions about Real Materials）

2025-07-10 カリフォルニア工科大学（Caltech）

Electron-phonon diagrams with four phonons (shown as wavy lines) interacting with electrons, evaluated using Diagrammatic Monte Carlo. Loop diagrams like the one shown here are used to compute electrical conductivity as a function of temperature (T=1/beta). The open diagram contributes to higher-order scattering of an electron with momentum k1 and the corresponding formation of a polaron.

＜関連情報＞

• https://www.caltech.edu/about/news/adding-up-feynman-diagrams-to-make-predictions-about-real-materials
• https://www.nature.com/articles/s41567-025-02954-1
• https://tiisys.com/blog/2024/05/29/post-138219/

電子-フォノン相互作用とポーラロンの第一原理計算モンテカルロ法 First-principles diagrammatic Monte Carlo for electron–phonon interactions and polaron

Yao Luo,Jinsoo Park & Marco Bernardi
Nature Physics  Published:10 July 2025
DOI:https://doi.org/10.1038/s41567-025-02954-1

Abstract

In condensed matter, phonons—quanta of the lattice vibration field—couple with electrons, leading to the formation of entangled electron–phonon states called polarons. In the intermediate- and strong-coupling regimes common to many conventional and quantum materials, a many-body treatment of polarons requires adding up a large number of electron–phonon Feynman diagrams. In this regard, diagrammatic Monte Carlo is an efficient method for diagram summation and has been used to study polarons within simplified electron–phonon models. Here we develop diagrammatic Monte Carlo calculations based on accurate first-principles electron–phonon interactions, enabling numerically exact results for the ground-state and dynamical properties of polarons in real materials. We implement these calculations in LiF, SrTiO₃, and rutile and anatase TiO₂, and describe both localized and delocalized polarons. Our work enables the precise modeling of electron–phonon interactions and polarons in coupling regimes ranging from weak to strong. The results will provide deeper insights into transport phenomena, linear response and superconductivity within the strong electron–phonon coupling regime.