Quasiparticle Interactions in the $S = 1/2$ Heisenberg Antiferromagnetic Chain CuPzN

Abstract

We investigate spinon--spinon interactions in the quasi-one-dimensional $S=1/2$ Heisenberg antiferromagnet Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$ (CuPzN) using inelastic neutron scattering. At zero field, the spectrum exhibits the canonical multi-spinon continuum of the Heisenberg chain. With increasing field we demonstrate the appearance of an energy gap $2\Delta$ towards momentum $q\rightarrow 0$ between the uniform magnetization precession mode and the shifted spinon continuum. $2\Delta$ is a direct measure of spinon backscattering interactions. Comparison with numerical matrix-product-state calculations and a recent analytical theory shows excellent agreement. By examining the integrable spin-1/2 chain, we provide an example of how quasiparticle interactions can be quantified experimentally in isotropic quantum spin systems.