Concurrence of finite Ising chains with the Dzyaloshinsky-Moriya interaction

Due to the great impact that quantum information theory has and its applicability for condensed matter systems, we study the concurrence measure of entanglement for the finite Ising chain with the Dzyaloshinsky-Moriya interaction. The explicit calculation of the concurrence and the reduced density matrix necessary to calculate it is presented, in order to use them as a pedagogical tool to make such important concepts clearer. A growth of the concurrence was observed as the parameter of the interaction increased, reaching a maximum at D = 1, which indicates the phase transition of the system from an antiferromagnetic phase to a chiral one.