Tentative structural features of a gapped RVB state in the anisotropic triangular lattice (original) (raw)
The self-consistency equations for the independent order parameters as well as the free energy expression for the mean-field RVB model of the spin-1/2 Heisenberg Hamiltonian on the anisotropic triangular lattice is considered in the quasi-one-dimensional approximation. The solutions of the self-consistency equations in the zero-temperature limit are in fair agreement with the previous numerical analysis of the same model by other authors. In particular, the transition from the ungapped 1D-RVB state to the gapped 2D-RVB state occurs at an arbitrarily weak transversal exchange (J 2 → 0) although the amount of the gap is exponentially small: 12J 1 π exp − 2J 1 J 2 , where J 1 is the longitudinal exchange parameter. The structural consequences of the formation of the 2D-RVB state are formulated by extending the famous bond order vs. bond length relation known for polyenes (onedimensional Hubbard chains). Analytical estimates of this effect are given.