Exact results for resonating valence bonds states on 2D (narrow) systems

It is shown that the problem of calculating spin-spin correlation functions, in the dimers RVB states, on a possibly diluted 2D square lattice, can be formulated in terms of a transfer matrix. The transfer matrix is used for exact numerical calculations of spin-spin correlation functions on ladders up to four units wide. Typeset using REVTEX 1 In the last few years, the class of Resonating Valence Bonds (RVB) states have drawn much attention in connection to the long lasting pursuit of the anti-ferromagnetic 2D Heisenberg model ground state [1,2]. Especially important is the case of spin half, which is considered to be relevant to high Tc superconductors. In this context, simulations had been performed to estimate the spin-spin correlation functions in these states [3]; and particularly the expectation values of the spin half Heisenberg Hamiltonian were calculated for variational considerations. In the two legged ladder lattice the short range RVB states, which are in the focus of this article, were found to have low energies [4]. Despite this interest these simulations had not been backed by exact results. This article provides a way to extract such results, in the case of the 2D dimers RVB states on a (possibly) diluted lattice, by means of reducing the problem of calculating the spin-spin correlation functions, to the considerably simpler problem of treating a transfer matrix defined on a 1D lattice. On a general lattice the class of RVB states is defined by [3] |Ψ〉 = ∑