Spin-wave analysis to the spatially anisotropic Heisenberg antiferromagnet on a triangular lattice

We study the phase diagram at $T=0\mathrm{}$ of the antiferromagnetic Heisenberg model on the triangular lattice with spatially anisotropic interactions. For values of the anisotropy very close to $J_{\alpha }{/J}_{\beta }=0.5,$ conventional spin-wave theory predicts that quantum fluctuations melt the classical structures, for $S=1/2.\mathrm{}$ For the regime $J_{\beta }<J_{\alpha },$ it is shown that the incommensurate spiral phases survive until $J_{\beta }{/J}_{\alpha }=0.27,$ leaving a wide region where the ground state is disordered. The existence of such nonmagnetic states suggests the possibility of spin-liquid behavior for intermediate values of the anisotropy.