# SciPost Commentary Page

### Original publication:

Title: | The four-spinon dynamical structure factor of the Heisenberg chain |

Author(s): | Jean-Sébastien Caux, Rob Hagemans |

As Contributors: | Jean-Sébastien Caux |

Journal ref.: | J. Stat. Mech. 2006, P12013 |

DOI: | http://dx.doi.org/10.1088/1742-5468/2006/12/P12013 |

Date: | 2006-12-18 |

### Abstract:

We compute the exact four-spinon contribution to the zero- temperature dynamical structure factor of the spin-1/2 Heisenberg isotropic antiferromagnet in zero magnetic field, directly in the thermodynamic limit. We make use of the expressions for matrix elements of local spin operators obtained by Jimbo and Miwa using the quantum affine symmetry of the model, and of their adaptation to the isotropic case by Abada, Bougourzi and Si-Lakhal (correcting some overall factors). The four-spinon contribution to the first frequency moment sum rule at fixed momentum is calculated. This shows, as expected, that most of the remaining correlation weight above the known two-spinon part is carried by four-spinon states. Our results therefore provide an extremely accurate description of the exact structure factor.

## Jean-Sébastien Caux on 2016-05-12 [id 44]

There is a typo in equation 31. The upper limits of the boundaries have been interchanged. The correct formula is

$$

\frac{\pi}{2} \sin k \leq \omega \leq \pi \cos \frac{k}{2}: \hspace{10mm} K \notin \left[ K^-_{2c}, K^+_{2c} \right] \cup \left[ K^-_{2c} + \pi, K^+_{2c} + \pi \right]

$$

followed by

$$

\frac{\pi}{2} \sin k \leq \omega \leq \pi \sin \frac{k}{2}: \hspace{10mm} K \notin \left[ K^-_{2d}, K^+_{2d} \right] \cup \left[ K^-_{2d} + \pi, K^+_{2d} + \pi \right]

$$