Entanglement entropy between short range correlations and the Fermi sea in nuclear structure

Abstract

The nuclear structure orbital entanglement entropy of short range correlation (SRC) is calculated based on the nuclear scale separation, specifically, the entanglement between the SRC orbitals and the rest of the system. It should be stressed that this is a single nucleon and not a pair entanglement entropy between the proton and neutron. The entanglement arises from the probability for a nucleon to occupy a momentum state above the Fermi momentum. The momentum space of the nucleus separates into two parts such that nucleons can occupy the mean-field part of the wave function, i.e., the Fermi sea (FS) and separately the high-momentum SRC part. The orbital entropy obtained is between these two parts where essentially two momentum subspaces are defined, one containing all the low momentum FS states and the other containing the high-momentum part as a SRC ``orbital'' state. For the calculation of the decoupling of low and high momenta which was established by the similarity normalization group the SRC is employed and viewed as a further orbital which can be multiply occupied. Since the probability of the occupation of a single SRC is given by the nuclear contact a simple general expression of the orbital entanglement entropy for SRC by employing the generalized contact formalism is obtained. This general formula for the SRC orbital entanglement entropy of a nuclear structure in terms of the nuclear contact allows one to obtain the scaling of the entropy in terms of the mass number, $A$. From this formula it is evident that, unlike the entanglement entropy of many quantum systems which scales with the surface area, the orbital entanglement entropy associated with the SRC in large nuclei is linearly dependent on $A$, i.e., it is shown to be extensive.