Bayesian Hamiltonian Selection in X-ray Photoelectron Spectroscopy

Core-level X-ray photoelectron spectroscopy (XPS) is a useful measurement technique for investigating the electronic states of a strongly correlated electron system. Usually, to extract physical information of a target object from a core-level XPS spectrum, we need to set an effective Hamiltonian by physical consideration so as to express complicated electron-to-electron interactions in the transition of core-level XPS, and manually tune the physical parameters of the effective Hamiltonian so as to represent the XPS spectrum. Then, we can extract physical information from the tuned parameters. In this paper, we propose an automated method for analyzing core-level XPS spectra based on the Bayesian model selection framework, which selects the effective Hamiltonian and estimates its parameters automatically. The Bayesian model selection, which often has a large computational cost, was carried out by the exchange Monte Carlo sampling method. By applying our proposed method to the 3$d$ core-level XPS spectra of Ce and La compounds, we confirmed that our proposed method selected an effective Hamiltonian and estimated its parameters appropriately; these results were consistent with conventional knowledge obtained from physical studies. Moreover, using our proposed method, we can also evaluate the uncertainty of its estimation values and clarify why the effective Hamiltonian was selected. Such information is difficult to obtain by the conventional analysis method.