Proton-neutron entanglement entropy in shell model calculations *

The entanglement entropy is a measure of the correlations between the components of a bipartite system: the lower the entropy, the more independent

the components are. We apply this concept in the shell model and compute the entropy of entanglement between the proton and neutron parts

of the many-body wave function. We find a strong connection between symmetry and entropy, and provide some speculations as to the origin of this connection.