Resonating Valence Bond Theory of Coupled Heisenberg Chains

Using numerical results from a density matrix renormalization group study as a guide, we develop a resonating valence bond (RVB) theory for coupled Heisenberg chains. We argue that simple topological effects mandate a short-range RVB description of systems with an even number of chains $n_c$, with a spin gap, short-range correlations, and confinement of topological spin defects. Odd-$n_c$ systems have long-range RVB ground states, no gap, and power-law correlations.