Ground State Phase Diagram of the Heisenberg Model on Anisotropic Triangular Lattice.

We study the spin-half and spin-one Heisenberg models on the anisotropic triangular lattice with interactions $J_1$ and $J_2$. The model interpolates between the limits of square lattice ($J_1=0$), triangular lattice ($J_1=J_2$) and decoupled one dimensional linear chains ($J_2=0$). Results are obtained by means of linked-cluster series expansions around the colinear antiferromagnetic phase (CAF) and the non colinear antiferromagnetic phase (NCAF), also known as the spiral phase. For the spin-half model, both phases can be stabilized within our calculations for small $J_2$. However, the NCAF phase always appears to have a lower energy. The pitch of the spiral is substantially renormalized from the classical values. For the spin-one model, we find a transition from the Haldane gap phase to the NCAF phase as a function of $J_1/J_2$. Interchain coupling required for this transition is more than a factor of $30$ larger than when the chains are coupled in an unfrustrated square-lattice geometry. The CAF phase does not appeared to be stabilized for any value of $J_1/J_2$ for the spin-one model.