Characterizing entanglement by momentum-jump in the frustrated Heisenberg ring at quantum phase transition

We study the pairwise concurrences, a measure of entanglement, of the ground states for the frustrated Heisenberg ring to explore the relation between entanglement and quantum phase transition associated with the momentum jump. The groundstate concurrences between any two sites are obtained analytically and numerically. It shows that the summation of all possible pairwise concurrences is an appropriate candidate to depict the phase transition. We also investigate the role that the momentum takes in the jump of concurrence at the critical points. We find that an abrupt momentum change rusults in the maximal concurrence difference of two degenerate ground states.