Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain

TL;DR

This paper demonstrates that the antiferromagnetic Heisenberg ladder is equivalent to a single $S=1$ chain through continuous transformations, showing they share the same phase and revealing stronger topological order in the ladder.

Contribution

It introduces two continuous transformations linking the $S=1$ chain and the $S=1/2$ ladder, establishing their phase equivalence and enhanced topological order.

Findings

Both systems are in the same phase.

Hidden topological order is stronger in the ladder.

Transformations couple next nearest neighbors to form $S=1$.

Abstract

I introduce two continuous transformations between the $S=1$ Heisenberg chain and the antiferromagnetic $S=1/2$ Heisenberg ladder. Both transformations couple diagonally situated {\it next nearest neighbor} $S=1/2$'s to form each $S=1$. Using the density matrix renormalization group, I demonstrate that the two systems are in the same phase. Furthermore, I find that the hidden topological long-range order characterizing the $S=1$ system is even stronger in the isotropic two-chain system.