Pairwise Entanglement and Local Polarization of Heisenberg Model

The pairwise entanglement and local polarization of the ground state are discussed by studying the Heisenberg XX model in finite qubit case. The results show that: the ground state is composed by the micro state with the minimal total spin 0 (for even qubit) or 1/2 (for odd qubit), local polarization (LP) has intimate relation with the probability of the micro state in the ground state, the stronger the LP the smaller the probability, the same LP corresponding to the same probability; the pairwise entanglement of the ground state is the biggest in all the eigenvectors. We find when the qubit is small, the degenerate of state will decrease the pairwise entanglement, there has great different between the odd and the even qubit chain; when the qubit number is big, the effect of qubit number to the pairwise entanglement will disappear, the limited value will be round about 0.3424.