Absence of gap for infinite half--integer spin ladders with an odd number of legs

TL;DR

This paper proves that infinite half-integer spin ladders with an odd number of legs have no energy gap, impacting the understanding of coupled one-dimensional spin systems in certain materials.

Contribution

It provides a rigorous proof of the absence of a gap in odd-leg half-integer spin ladders, clarifying their low-energy behavior.

Findings

No energy gap exists for odd-leg half-integer spin ladders.

Results are relevant to specific materials like vanadyl pyrophosphate and certain cuprates.

Supports the theoretical understanding of coupled spin systems.

Abstract

A proof is presented for the absence of gap for spin $1/2$ ladders with an odd number of legs, in the infinite leg length limit. This result is relevant to the current discussion of coupled one--dimensional spin systems, a physical realization of which are vanadyl pyrophosphate, (VO)$_2$P$_2$O$_7$, and stoichiometric Sr$_{n-1}$ Cu$_{n+1}$ O$_{2n}$ (with $n=3,5,7,9,\dots$).