Integrable su(2)-invariant spin chains and the Haldane conjecture

TL;DR

This paper systematically searches for integrable, isotropic spin-S chains, supporting the classification of such chains and discussing their properties in relation to the Heisenberg model.

Contribution

It provides a comprehensive algebraic classification of su(2)-invariant integrable spin chains for spins less than 14, advancing understanding of their structure.

Findings

Identification of new integrable spin chains for S < 14

Support for the complete classification of su(2)-invariant chains

Insights into the spin-dependent properties of the Heisenberg chain

Abstract

We perform a systematic exact algebraic search for integrable spin-S chains which are isotropic in spin space, i.e. are su(2)-invariant. The families of spin chains found for S < 14 support recent arguments in favour of the complete classification of all such integrable chains. The integrable families of spin chains are discussed in the light of the conjectured spin-dependent properties of the Heisenberg chain.