The Heisenberg model with competing exchanges together with the chiral term is studied using series expansion about the dimer limit and by finite-size diagonalizations. The phase diagram is determined with ground-state orderings and the lowest excitation characteristics. We find that the chiral term induces a gapless line in frustrated spin-gapped phases. A critical chiral strength is also able to change the ground state from spiral to Neel quasi-long-range-order phase.
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