Machine-learning test of the single-ion model for $dd$ excitations in cuprates

Abstract

We investigate $dd$ excitations in Resonant Inelastic X-ray Scattering spectra of YBa${}_2$Cu${}_3$O${}_6$ and La${}_2$CuO${}_4$ using the local single-ion model. The data are analyzed by conventional global fitting and by a convolutional neural network trained within the same theoretical framework. For YBa${}_2$Cu${}_3$O${}_6$, the excited state energies obtained with the two methods coincide, leading to the $xy$, $3z^2-r^2$, $xz/yz$ sequence for increasing energy. This result validates the use of machine learning tools for the analysis of RIXS spectra dominated by $dd$ excitations. By contrast, for La${}_2$CuO${}_4$, the two methods do not converge to a single solution, revealing the limitations of the single-ion model in describing $dd$ excitations in cuprates and pointing to the role of additional contributions beyond a purely local picture in shaping high-energy excitations.