The four-spinon dynamical structure factor of the Heisenberg chain

Abstract

We compute the exact four-spinon contribution to the zero-temperature dynamical structure factor of thespin-1/2 Heisenberg isotropic antiferromagnet in zero magnetic field, directly in the thermodynamiclimit. We make use of the expressions for matrix elements of local spin operators obtainedby Jimbo and Miwa using the quantum affine symmetry of the model, and of theiradaptation to the isotropic case by Abada, Bougourzi and Si-Lakhal (correcting someoverall factors). The four-spinon contribution to the first frequency moment sum rule atfixed momentum is calculated. This shows, as expected, that most of the remainingcorrelation weight above the known two-spinon part is carried by four-spinon states. Ourresults therefore provide an extremely accurate description of the exact structure factor.