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We have studied occurrence of quantum phase transition in the one-dimensionalspin-1/2 Ising model with added Dzyaloshinsky-Moriya (DM) interaction from bi-partite and multi-partite entanglement point of view. Using exact numericalsolutions, we are able to study such systems up to 24 qubits. The minimum ofthe entanglement ratio R $\equiv$ \tau 2/\tau 1 < 1, as a novel estimator ofQPT, has been used to detect QPT and our calculations have shown that itsminimum took place at the critical point. We have also shown both theglobal-entanglement (GE) and multipartite entanglement (ME) are maximal at thecritical point for the Ising chain with added DM interaction. Using matrixproduct state approach, we have calculated the tangle and concurrence of themodel and it is able to capture and confirm our numerical experiment result.Lack of inversion symmetry in the presence of DM interaction stimulated us tostudy entanglement of three qubits in symmetric and antisymmetric way whichbrings some surprising results.

Entanglement study of the 1D Ising model with Added Dzyaloshinsky-Moriya interaction