Quantum corrections of the Dzyaloshinskii-Moriya interaction on the   spin-1/2 AF-Heisenberg chain in an uniform magnetic field
  We have investigated the ground state phase diagram of the 1D AF spin-1/2 Heisenberg model with the staggered Dzyaloshinskii-Moriya (DM) interaction in an external uniform magnetic field $H$. We have used the exact diagonalization technique. In the absence of the uniform magnetic field (H=0), we have shown that the DM interaction induces a staggered chiral phase. The staggered chiral phase remains stable even in the presence of the uniform magnetic field. We have identified that the ground state phase diagram consists of four Luttinger liquid, staggered chiral, spin-flop, and ferromagnetic phases. 
S. Mahdavifar, M. R. Soltani and A. A. Masoudi