The electronic correlation strength is a basic quantity that characterizes the physical properties of materials such as transition metal oxides. Determining correlation strengths requires both precise definitions and a careful comparison between experiment and theory. In this paper we define the correlation strength via the magnitude of the electron self-energy near the Fermi level. For the case of LaNiO$_3$, we obtain both the experimental and theoretical mass enhancements $m^star/m$ by considering high resolution angle-resolved photoemission spectroscopy (ARPES) measurements and density functional + dynamical mean field theory (DFT + DMFT) calculations. We use valence-band photoemission data to constrain the free parameters in the theory, and demonstrate a quantitative agreement between the experiment and theory when both the realistic crystal structure and strong electronic correlations are taken into account. These results provide a benchmark for the accuracy of the DFT+DMFT theoretical approach, and can serve as a test case when considering other complex materials. By establishing the level of accuracy of the theory, this work also will enable better quantitative predictions when engineering new emergent properties in nickelate heterostructures.
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