  Based on exact diagonalization and density matrix renormalization group
(DMRG) method, we show that an anisotropic triangle lattice Heisenberg spin
model has three distinct quantum phases. In particular, a spin-liquid phase is
present in the weak interchain coupling regime, which is characterized by an
exponentially-decaying spin correlator along the weaker coupling direction and
a quasi-one-dimensional spin structure factor along the chain direction, in
agreement with experiments on the Cs2CuCl4 compounds. In the obtained phase
diagram, the spin liquid phase is found to persist up to a relatively large
critical anisotropic coupling ratio J'/J=0.78, which is stabilized by strong
quantum fluctuations, with a parity symmetry distinct from two magnetic ordered
states in the stronger coupling regime.
