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The self-consistency equations for the independent order parameters as wellas the free energy expression for the mean-field RVB model of the spin-1/2Heisenberg Hamiltonian on the anisotropic triangular lattice is considered inthe quasi-one-dimensional approximation. The solutions of the self-consistencyequations in the zero-temperature limit are in fair agreement with the previousnumerical analysis of the same model by other authors. In particular, thetransition from the ungapped 1D-RVB state to the gapped 2D-RVB state occurs atan arbitrarily weak transversal exchange ($J_{2}\rightarrow0)$ although theamount of the gap is exponentially small:$\frac{12J_{1}}{\pi}\exp(-\frac{2J_{1}}{J_{2}})$, where $J_{1}$ is thelongitudinal exchange parameter. The structural consequences of the formationof the 2D-RVB state are formulated by extending the famous bond order\emph{vs}. bond length relation known for polyenes (one-dimensional Hubbardchains). Analytical estimates of this effect are given.

Tentative Structural Features of a Gapped RVB State in the Anisotropic Triangular Lattice