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

Abstract

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 ($J_2\to 0)$ although the amount of the gap is exponentially small: $\frac{12J_1}{\pi }\exp (-\frac{2J_1}{J_2})$, 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 \emph{vs}. bond length relation known for polyenes (one-dimensional Hubbard chains). Analytical estimates of this effect are given.

14 pages, 2 figures

References in corpus (2)

• Mutant knots and intersection graphs
• On the Properties of the Longitudinal RVB State in the Anisotropic Triangular Lattice. Mean-Field RVB Analytical Results

Cited by in corpus (1)

• c-a-ca Mean Field RVB Model of CuNCN Physics. Structure Manifestations of the RVB Transitions