Finite temperature structure factor in the Haldane-Shastry spin chain

TL;DR

This paper computes the finite temperature spin structure factor of the Haldane-Shastry chain using Jack polynomial techniques, providing convergent form factor expansions and numerical results for static and dynamic properties.

Contribution

It introduces a novel application of $rak{gl}_2$ Jack polynomials to calculate form factors and structure factors in the Haldane-Shastry model at finite temperature.

Findings

Form factor expansion converges at small momentum.

Numerical results approximate the infinite temperature structure factor.

Method provides a new way to analyze integrable spin chains.

Abstract

The Haldane-Shastry spin chain can be mapped to the infinite coupling limit of the SU(2) spin Calogero-Sutherland model. We use the $\mathfrak{gl}_2$ Jack polynomials' technology to compute the form factors of the spin operator on the multi-spinon spectrum. The spin structure factor is obtained through a form factor expansion. The expansion is proven to converge in the small momentum limit. Numerics based on two- and four-spinons contributions give an approximate result for the infinite temperature static and dynamic spin structure factor.