Resonating Valence Bond Theory of Coupled Heisenberg Chains

TL;DR

This paper develops an RVB theory for coupled Heisenberg chains, revealing that even and odd numbers of chains exhibit fundamentally different quantum states, with implications for spin gaps and correlations.

Contribution

It introduces a topologically motivated RVB framework for coupled chains, distinguishing between gapped even-chain and gapless odd-chain systems.

Findings

Even-chain systems have a spin gap and short-range correlations.

Odd-chain systems exhibit long-range RVB states with no gap.

The theory aligns with numerical DMRG results.

Abstract

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.