The 4-spinon dynamical structure factor of the Heisenberg chain

TL;DR

This paper calculates the exact 4-spinon contribution to the dynamical structure factor of the spin-1/2 Heisenberg chain at zero temperature, revealing that 4-spinon states carry most of the remaining correlation weight beyond 2-spinon contributions.

Contribution

It provides the first exact computation of the 4-spinon part of the structure factor in the thermodynamic limit for the Heisenberg chain, improving understanding of multi-spinon excitations.

Findings

Most of the remaining correlation weight is carried by 4-spinon states.

The 4-spinon contribution accurately describes the structure factor.

The calculation confirms the significance of 4-spinon states beyond 2-spinon contributions.

Abstract

We compute the exact 4-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 4-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 2-spinon part is carried by 4-spinon states. Our results therefore provide an extremely accurate description of the exact structure factor.