Is the purely biquadratic spin 1 chain always massive?

TL;DR

This paper demonstrates that the purely biquadratic spin 1 chain can be gapless when it has open boundaries and an odd length, challenging the assumption that such chains are always massive.

Contribution

It establishes a connection between the XXZ spin chain with boundary fields and the biquadratic spin 1 chain, revealing conditions for gapless behavior.

Findings

Gapless sector exists in odd-length biquadratic spin 1 chains with open boundaries.

Spectral equivalence via Temperley-Lieb algebra links the XXZ and biquadratic chains.

Contradicts the common belief that purely biquadratic spin 1 chains are always gapped.

Abstract

It is shown that the sl(2)q-invariant open antiferromagnetic XXZ spin chain with a boundary field has a gapless sector in the thermodynamic limit when its length is odd. Owing to a Temperley-Lieb equivalence of the spectra, the same conclusion is drawn for the purely biquadratic spin 1 chain with open boundaries and odd length.