Multireference density functional theory (MR-DFT) has been a pivotal method for studying nuclear low-lying states and neutrinoless double-beta ($0\nu \beta \beta$) decay. However, quantifying their theoretical uncertainties has been a significant challenge due to the computational demands. This study introduces a subspace-projected covariant density functional theory (SP-CDFT), which efficiently emulates MR-CDFT calculations for nuclear low-lying states. This approach leverages the eigenvector continuation method combined with the quantum-number projected generator coordinate method, based on a relativistic energy density functional (EDF). We apply SP-CDFT to investigate the correlations among the physical quantities of nuclear matter, nuclear low-lying spectroscopy, and the nuclear matrix elements (NMEs) of $0\nu \beta \beta$ decay in the two heaviest candidate nuclei. Our findings reveal generally strong correlations between the NMEs of $0\nu \beta \beta$ decay and the excitation energy of the $2_1^{+}$ state, as well as the $E2$ transition strength, although these correlations vary significantly among nuclei. This work also paves the way for refining nuclear EDF parameters using spectroscopic data.

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• Nuclear structure & decays
• Many-body techniques
• Nuclear density functional theory