Subspace-projected multireference covariant density functional theory

Multireference density functional theory (MR-DFT) has been a pivotal method for studying nuclear spectroscopy and neutrinoless double-beta (0νββ) 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 0νββ decay in the two heaviest candidate nuclei. Our findings reveal generally strong correlations between the NMEs of 0νββ decay and the excitation energy of the 2₁⁺ state, as well as the $E2$ transition strength, although these correlations vary significantly among nuclei. The Bayesian analysis, which integrates the properties of nuclear matter and low-lying states, yields mean values and statistical uncertainties for the NMEs 4.33(5) for ¹³⁶Xe and 5.51(14) for ¹⁵⁰Nd. This work also paves the way for refining nuclear EDF parameters using spectroscopic data.