Bridging Materials, Models, and Spectra with First-Principles Downfolding and Machine Learning*

Material properties are probed by various spectroscopy methods. It is thus highly desirable yet challenging to predicting spectral functions for strongly correlated systems, and it is even more difficult to address the inverse problem, namely predicting the realistic material parameters from given spectral functions. In this talk, we show that the problems could be accurately handled by encoding computational materials data to low-energy effective Hamiltonians and then machine learning the relationship between the small number of Hamiltonian parameters and the whole spectral functions including their characteristic incoherent parts. This approach will be examined in detail, with cuprate superconductors as a canonical example, from the first-principles guided derivation of the t-t'-t''-J model to machine learning the spectral functions relevant to X-ray photoelectron spectroscopy (XPS) and angular-resolved photoemission spectroscopy (ARPES). The results suggest the use of deep-learning methods to predict material parameters from experimentally measured spectral functions.