Shareability of quantum correlations in a many-body spin system with two- and three-body interactions

The shareability of quantum correlations among the constituent parties of a multiparty quantum system is restricted by the quantum information theoretic concept called monogamy. Depending on the multiparty quantum systems, different measures of quantum correlations show disparate signatures for monogamy. We characterize the shareability of quantum correlations, from both entanglement-separability and information-theoretic kinds, in a multiparty quantum spin system containing two- and three-body interactions with respect to its system parameters and external applied magnetic field. Monogamy score in this system exhibits both monogamous and nonmonogamous traits depending on the quantum correlation measure, strengths of system parameters, and external magnetic field. The percentage of nonmonogamous states when the information-theoretic quantum correlations are considered is higher than that of the entanglement-separability kind in allowed ranges of these variables. The integral powers of the quantum correlation measures for which the nonmonogamous states become monogamous are identified.