Adjacent Spin Operator Dynamical Structure Factor of the S=1/2 Heisenberg Chain

TL;DR

This paper computes the dynamical structure factors for adjacent spin operators in the S=1/2 Heisenberg chain, revealing significant 4-spinon contributions and analyzing excitation types across magnetic fields.

Contribution

It provides a determinant representation of form factors for specific spin operators and analyzes their dynamical structure factors throughout the Brillouin zone.

Findings

The $S^z_jS^z_{j+1}$ structure factor has a large 4-spinon contribution.

4-spinon excitations are distinguishable from 2-spinon signals.

The analysis covers various magnetic fields and excitation types.

Abstract

Considering the adjacent spin operators $S^z_jS^z_{j+1}$ and $S^-_jS^-_{j+1}$ in the S=1/2 Heisenberg chain, we give a determinant representation of their form factors. The dynamical structure factors of the respective operators are computed over the whole Brillouin zone in several magnetic fields and the resulting signal is analyzed in terms of excitation types. Among other results, we find that the $S^z_jS^z_{j+1}$ dynamical structure factor carries a large weight of the 4-spinon excitations which are distinguishable from the 2-spinon signal because they are located outside the 2-spinon spectrum.