The Short-Range Correlations between nucleons in nuclei is regarded as a complex system. We investigate the relationship between the orbital entanglement entropy of SRCs Sij in nuclear structures and Tan contact cij, and find that the orbital entanglement entropies and Tan contacts corresponding to proton-proton SRC pairs and neutron-proton SRC pairs in nuclei demonstrate a scaling relation. More specifically, the proportionality of entanglement entropy between proton-proton pairs and neutron-proton pairs is directly related to the ratio of nuclear contacts within the atomic nucleus, demonstrating an approximate ratio of 2.0. Our research suggests that this scaling relationship should hold true for all symmetric nuclei, furthermore, we offer a possible explanation for this phenomenon.
The Short-Range Correlations between nucleons in nuclei is regarded as a complex system. We investigate the relationship between the orbital entanglement entropy of SRCs Sij in nuclear structures and Tan contact cij, and find that the orbital entanglement entropies and Tan contacts corresponding to proton-proton SRC pairs and neutron-proton SRC pairs in nuclei demonstrate a scaling relation. More specifically, the proportionality of entanglement entropy between proton-proton pairs and neutron-proton pairs is directly related to the ratio of nuclear contacts within the atomic nucleus, demonstrating an approximate ratio of 2.0. Our research suggests that this scaling relationship should hold true for all symmetric nuclei, furthermore, we offer a possible explanation for this phenomenon.
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.
For quantum many-body systems with short-range correlations (SRCs), the intimate relationship between their magnitude, the behavior of the single-particle occupation probabilities at momenta larger than the Fermi momentum, and the entanglement entropy is a new qualitative aspect not studied and exploited yet. A large body of recent condensed matter studies indicates that the time evolution of the entanglement entropy describes the nonequilibrium dynamics of isolated and strongly interacting many-body systems, in a manner similar to the Boltzmann entropy, which is strictly defined for dilute and weakly interacting many-body systems. Both theoretical and experimental studies in nuclei and cold atomic gases have shown that the fermion momentum distribution has a generic behavior n(k)=C/k4 at momenta larger than the Fermi momentum, due to the presence of SRCs, with approximately 20% of the particles having momenta larger than the Fermi momentum. The presence of the long momentum tails in the presence of SRCs changes the textbook relation between the single-particle kinetic energy and occupation probabilities, ${n}_{\text{mf}}(k)=1/{1+exp\ensuremath{\beta}[\ensuremath{\epsilon}(k)\ensuremath{-}\ensuremath{\mu}]}$ for momenta very different form the Fermi momentum, particularly for dynamics processes. SRCs induced high-momentum tails of the single-particle occupation probabilities increase the entanglement entropy of fermionic systems, which in its turn affects the dynamics of many nuclear reactions, such as heavy-ion collisions and nuclear fission.
Abstract Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton–proton and neutron–neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.
Proton-neutron pairing and like-nucleon pairing are two different facets of atomic nuclear configurations. While like-nucleon pair condensates manifest their superfluidic nature in semimagic nuclei, it is not absolutely clear if there exists a T=0 proton-neutron pair condensate phase in N=Z nuclei. With an explicit formalism of general pair condensate with good particle numbers, we optimize proton-neutron pair condensates for all N=Z nuclei between 16O and 100Sn, given shell model effective interactions. As comparison, we also optimize like-nucleon pair condensates for their semimagic isotones. Shannon entanglement entropy is a measurement of mixing among pair configurations, and can signal intrinsic phase transition. It turns out the like-nucleon pair condensates for semimagic nuclei have large entropies signaling an entangled phase, but the proton-neutron pair condensates end up not far from a Hartree-Fock solution with small entropy. With artificial pairing interaction strengths, we show that the general proton-neutron pair condensate can transit from an entangled T=1 phase to an entangled T=0 phase, i.e., pairing phase transition driven by external parameters. In the T=0 limit, the proton-neutron pair condensate optimized for 24Mg turns out to be a purely T=0 P-pair condensate with large entanglement entropy, although such cases may occur in cold atom systems, unlikely in atomic nuclei.
Background: The high-momentum distribution of atoms in two spin-state ultracold atomic gases with strong short-range interactions between atoms with different spins, which can be described by using Tan's contact, are dominated by short-range pairs of different fermions and decreases as ${k}^{\ensuremath{-}4}$. In atomic nuclei the momentum distribution of nucleons above the Fermi momentum ($k>{k}_{F}\ensuremath{\approx}250$ MeV/c) is also dominated by short-range-correlated different-fermion (neutron-proton) pairs.Purpose: Compare high-momentum unlike-fermion momentum distributions in atomic and nuclear systems.Methods: We show that, for k>kF MeV/c, nuclear momentum distributions are proportional to that of the deuteron. We then examine the deuteron momentum distributions derived from a wide variety of modern nucleon-nucleon potentials that are consistent with NN-scattering data.Results: The high-momentum tail of the deuteron momentum distribution, and hence of the nuclear momentum distributions, appears to decrease as ${k}^{\ensuremath{-}4}$. This behavior is shown to arise from the effects of the tensor part of the nucleon-nucleon potential. In addition, when the dimensionless interaction strength for the atomic system is chosen to be similar to that of atomic nuclei, the probability for finding a short-range different-fermion pair in both systems is the same.Conclusions: Although nuclei do not satisfy all of the conditions for Tan's contact, the observed similarity of the magnitude and ${k}^{\ensuremath{-}4}$ shape of nuclear and atomic momentum distributions is remarkable because these systems differ by about 20 orders of magnitude in density. This similarity may lead to a greater understanding of nuclei and the density dependence of nuclear systems.
Quantum entanglement provides a unique perspective for probing nuclear structure. In this work, we employ quantum entanglement measures, including proton-neutron entanglement entropy, mutual information, and quantum relative entropy, to investigate the evolution of entanglement patterns as we approach neutron-rich nuclei. The study is carried out in the vicinity of the N=20 island of inversion region consisting of even-A Ne, Mg, and Si isotopes, and also for isotones corresponding to N=20. The state-of-the-art \textit{ab initio} valence space in-medium similarity renormalization group method has been used for this purpose. We have highlighted the role of proton-neutron entanglement entropy in the formation of the island of inversion region. Mutual information provides insight into the strength of correlations between proton-proton, neutron-neutron, and proton-neutron single-particle states. While these correlations are relatively weak between protons and neutrons in the ground states, they become comparable to like-particle correlations in excited states. The quantum relative entropy is also studied between 0+ and 2+ states of the Ne, Mg, and Si isotopes, as well as N=20 isotones, using the Kullback-Leibler divergence and Jensen-Shannon divergence. We have performed these calculations by expressing the nuclear wavefunctions in a Slater-determinant basis and analyzing them through complementary partitions, including proton-neutron and mode-resolved factorizations.