entanglement in the xz spin chain model in the external magnetic field

the entanglement at zero-temperature is studied in a two-qubit xz spin-1/2 chain model in anexternal magnetic field which is applied in the z direction. we have obtained an analytical relation forthe effect of the external magnetic field on the concurrence. it is shown that the ground state of thesystem depends on the strength of exchange coupling. we have shown that the analytical relation ofthe concurrence is independent of jz. it is shown that for jz >0 the concurrence is depended on thecritical value of the external magnetic field and it is changed at the critical external magnetic field.also we have shown that for h hc, the concurrence decreases by increasing theexternal magnetic field. for jz