Quantitative measure of correlation strength among intertwined many-body interactions

The intertwined coupling among various many-body interactions is increasingly recognized as playing a key role in strongly correlated electron systems. However, understanding their relationship to physical properties is challenging due to the lack of a definitive experimental measure. Here, we report an analytical approach that utilizes machine learning to enable a higher level of evaluation of many-body interactions through a large amount of data from a single material using spatially resolved and angle-resolved photoemission spectroscopy. We demonstrate that various physical parameters, including the coupling strengths of electron-electron and electron-boson interactions, can be statistically evaluated, and the correlation between many-body interactions can also be accessed. Our approach thus provides a quantitative measure of the microscopic variables and serves as a linking bridge between them, holding great promise in disentangling the complex nature of strongly correlated materials where many-body interactions generally mutually interplay.