Spin Currents Carried by Spinons in XXZ Spin Chains: Signatures in Polarized Inelastic Neutron Scattering

Quantum spin chains serve as a paradigm for exploring truly quantum phenomena, with spinons being the elementary excitations. Motivated by compounds such as CsCoBr$_3$ and CsCoCl$_3$, we focus on the Ising-like antiferromagnetic Heisenberg $XXZ$ model (spin-1/2). Here we present theoretical results for the total inelastic scattering cross section of spin-polarized neutrons in the presence of an external magnetic field, which is applied transverse to the Ising direction. In particular, we identify the spin current associated with spinons and their corresponding signatures in the neutron scattering cross section. The presence of a transverse magnetic field no longer allows for reliance on $S^{z}_{{\rm tot}}$ as a conserved quantity, which has traditionally been assumed in this context. As a striking consequence, we find that the spinons carry a non-vanishing spin current, even in the limit of infinitesimal fields. Our results are shown to be in good agreement with experimental neutron scattering data on CsCoBr$_3$.