Entanglement Suppression and Emergent Symmetries of Strong Interactions

Entanglement suppression in the strong-interaction $S$ matrix is shown to be correlated with approximate spin-flavor symmetries that are observed in low-energy baryon interactions, the Wigner $SU(4)$ symmetry for two flavors and an $SU(16)$ symmetry for three flavors. We conjecture that dynamical entanglement suppression is a property of the strong interactions in the infrared, giving rise to these emergent symmetries and providing powerful constraints that predict the nature of nuclear and hypernuclear forces in dense matter.

Figure 1

The entanglement power $\mathcal{E}(\widehat{\mathbf{S}})$ of the $S$ matrix as a function of $p$, the center-of-mass nucleon momentum. The ${}^1{S}_0$ and ${}^3{S}_1$ phase shifts used to calculate $\mathcal{E}(\widehat{\mathbf{S}})$ were taken from four different models [53, 54, 55, 56, 57] to provide a naïve estimate of systematic uncertainties. Data for this figure may be found in Table 2 in Supplemental Material [58].

Figure 2

Density plot of the entanglement power $\mathcal{E}(\widehat{\mathbf{S}})$ of the $S$ matrix (see Eq. (7) in Supplemental Material [58]) integrated over center-of-mass momenta $0\le p\le m_{\pi }/2$ versus the Lagrangian couplings ${\overline{C}}_0/C_{\star }$ and ${\overline{C}}_1/C_{\star }$, where $C_{\star }$ is the critical coupling for unitary scattering. The entanglement power vanishes at the four conformal fixed points (white points) as well as the fixed line corresponding to Wigner $SU(4)$ symmetry (white diagonal line).