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We have considered the 1D spin-(1/2) Heisenberg model with added Dzyaloshinskii-Moriya interaction. The effect of a uniform magnetic field on the ground state phase diagram of the model is studied. We have mapped the model to an effective model which is known as the 1D XXZ in both uniform and staggered magnetic fields. By selecting a block of two or three spins, we have solved the Hamiltonian exactly. Our results show that the quantum phase transitions can be obtained from the block of pair or three spins.

Heisenberg Model with Added Dzyaloshinskii-Moria Interaction