Minimal entanglement and emergent symmetries in low-energy QCD

We study low-energy scattering of spin-$\frac{1}{2}$ baryons from the perspective of quantum information science, focusing on the correlation between entanglement minimization and the appearance of accidental symmetries. The baryon transforms as an octet under the $\mathrm{SU}\left(3\right)$ flavor symmetry and its interactions below the pion threshold are described by contact operators in an effective field theory (EFT) of QCD. Despite there being 64 channels in the 2-to-2 scattering, only six independent operators in the EFT are predicted by $\mathrm{SU}\left(3\right)$. We show that successive entanglement minimization in $\mathrm{SU}\left(3\right)$-symmetric channels are correlated with increasingly large emergent symmetries in the EFT. In particular, we identify scattering channels whose entanglement suppression are indicative of emergent $\mathrm{SU}\left(6\right), \mathrm{SO}\left(8\right), \mathrm{SU}\left(8\right)$, and $\mathrm{SU}\left(16\right)$ symmetries. We also observe the appearance of non-relativistic conformal invariance in channels with unnaturally large scattering lengths. Improved precision from lattice simulations could help determine the degree of entanglement suppression, and consequently the amount of accidental symmetry, in low-energy QCD.