The Entanglement Entropy between Short Range Correlations and the Fermi Sea in Nuclear Structure

Abstract

We calculate the nuclear structure orbital entanglement entropy of short range correlations (SRC) 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 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. We separate the momentum space of the nucleus into two parts such that nucleons can occupy the meanfield part of the wave function, i.e. Fermi sea (FS) and separately the high-momentum SRC part. The orbital entropy we obtain is between these two parts where we essentially define two momentum subspaces, one containing all the low momentum FS states and the other the high-momentum part as a SRC "orbital" state. For the calculation we employ the decoupling of low and high-momenta which was established by the similarity normalization group the SRC is 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 we are able to obtain a simple general expression of the orbital entanglement entropy for SRC by employing the generalized contact formalism. This general formula for the SRC orbital entanglement entropy of a nuclear structure in terms of the nuclear contact, allows us to obtain the scaling of the entropy in terms the mass number, $A$. We find 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.

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