Exact four-spinon dynamical correlation function in isotropic Heisenberg model

Abstract

We discuss some properties of the exact four-spinon dynamical correlation function $S_4$ in the antiferromagnetic spin 1/2 $XXX$-model, the expression of which we derived recently. We show that the region in which it is not identically zero is different from and larger than the spin-wave continuum. We describe its behavior as a function of the neutron momentum transfer $k$ for fixed values of the neutron energy $ω$ and compare it to the one corresponding to the exact two-spinon dynamical correlation function $S_2$. We show that the overall shapes are quite similar, even though the expression of $S_4$ is much more involved than that of $S_2$. We finish with concluding remarks.