Dimerized phase of the spin-1/2 anisotropic triangular lattice antiferromagnet.

With Cs$_2$CuCl$_4$ in mind, we analyze quasi-one-dimensional limit of the quantum $S=1/2$ antiferromagnet on a triangular lattice. In this limit, the system can be viewed as a collection of parallel Heisenberg spin chains (exchange $J$) coupled by a weak zig-zag inter-chain exchange $J'$. We demonstrate, using renormalization group considerations and the Haldane-Shastry chain (which is equivalent to the Heisenberg one at low energies), that a marginally relevant ``twist" interaction between nearest chains generates a {\it relevant} interaction between staggered dimerizations on the next-nearest chains. This, previously overlooked, interaction appears to drive the system into a two-dimensional valence-bond solid phase with staggered ordering of dimerizations on next-nearest chains. The effect of weak further neighbor and Dzyaloshinskii-Moriya interactions in the anisotropic limit will also be discussed.