By using variational wave functions and quantum Monte Carlo techniques, we
investigate the complete phase diagram of the Heisenberg model on the
anisotropic triangular lattice, where two out of three bonds have
super-exchange couplings J and the third one has instead J′. This
model interpolates between the square lattice and the isotropic triangular one,
for J′/J≤1, and between the isotropic triangular lattice and a set
of decoupled chains, for J/J′≤1. We consider all the
fully-symmetric spin liquids that can be constructed with the fermionic
projective-symmetry group classification [Y. Zhou and X.-G. Wen,
arXiv:cond-mat/0210662] and we compare them with the spiral magnetic orders
that can be accommodated on finite clusters. Our results show that, for
J′/J≤1, the phase diagram is dominated by magnetic orderings, even
though a spin-liquid state may be possible in a small parameter window, i.e.,
0.7≲J′/J≲0.8. In contrast, for J/J′≤1, a
large spin-liquid region appears close to the limit of decoupled chains, i.e.,
for J/J′≲0.6, while magnetically ordered phases with spiral
order are stabilized close to the isotropic point.Comment: 11 pages, 11 figure