Pairwise entanglement and local polarization of Heisenberg model

Abstract

The characteristics of pairwise entanglement and local polarization (LP) are discussed by studying the ground state (states) of the Heisenberg XX model. The results show that: the ground state (states) is (are) composed of the micro states with the minimal polarization (0 for even qubit and 1/2 for odd qubit); LP and the probability of the micro state have an intimate relation, i.e. the stronger the LP, the smaller the probability, and the same LP corresponds to the same probability; the pairwise entanglement of the ground state is the biggest in all eigenvectors. It is found that the pairwise entanglement is decreased by the state degeneracy and the system size. The concurrence approaches a fixed value of about 0.3412 (for odd-qubit chain) or 0.3491 (for even-qubit chain) if the qubit number is large enough.