Exact Results of Dimerization Order Parameter in $SU(n)$ Antiferromagnetic Chains

TL;DR

This paper derives exact expressions for the dimerization order parameter in $SU(n)$ antiferromagnetic chains, linking it to staggered magnetization in related spin-$1/2$ $XXZ$ chains, providing fundamental insights into quantum spin systems.

Contribution

It establishes a direct proportionality between the dimerization order parameter in $SU(n)$ chains and the staggered magnetization in $SU(2)$ $XXZ$ chains, offering exact results for these quantum models.

Findings

Exact proportionality between dimerization order parameter and staggered magnetization.

Analytical expressions for the order parameter in the thermodynamic limit.

Connection between $SU(n)$ chains and $XXZ$ models clarified.

Abstract

After a proper definition of the dimerization order parameter for a spin-$S$ system, I show that this order parameter in the $SU(n)$ ($n=2S+1$) antiferromagnetic chains (or equivalently the $SU(2)$ spin-$S$ chains with Hamiltonians which project out singlet states) is, in the thermodynamic limit, directly proportional to the staggered-magnetization in the corresponding spin-$1\over2$ $XXZ$ chains which had already been mapped onto the $SU(n)$ chains.