Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons

TL;DR

This paper provides an exact calculation of the dynamical spin correlation function for a one-dimensional S=1/2 antiferromagnetic Heisenberg chain, revealing a simple integral form based on two-spinon states.

Contribution

It presents the first exact analytical expression for the ground-state dynamical structure factor of a gapless S=1/2 antiferromagnetic chain with free spinons, specifically for the Haldane-Shastry model.

Findings

S(Q,E) is exactly computed as a simple integral over two-spinon states.

The model's dynamical structure factor matches the low-energy universality class of the Bethe chain.

Only two-spinon states contribute to the dynamical structure factor.

Abstract

We calculate the exact dynamical magnetic structure factor S(Q,E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q,E) is found to be a very simple integral over these states.