Entanglement Entropy of Proton and Neutron Wave Functions in Atomic Nuclei

Entanglement entropy is a measure of the amount of information shared between two subsystems of a bipartite system. It can be shown that the representations of bipartite wave functions with lower entanglement entropy are dominated by fewer terms than ones with higher entanglement entropy. We compute the entanglement entropy between protons and neutrons in nuclear configuration-interaction wave functions and we find that the entanglement entropy decreases with increasing isospin. This suggests that N > Z nuclei will have even more efficient representations than N = Z nuclei in a proton-neutron factorization scheme, of the kind suggested by the singular- value-decomposition work of Papenbrock et al. Here we take a more in depth look at the entanglement entropy of configuration-interaction wave functions and explain our observations with the aid of a toy model.