Relationship between susceptibility and spin stiffness of mesoscopic quantum antiferromagnets

We investigate the quantum antiferromagnetic Heisenberg spin chain of integer spinS in the semiclassical limit (S 1) for a non-uniform system of finite-size and temperature. At low temperatures and in the mesoscopic regime with the correlation length being larger than the characteristic system size, boundary conditions significantly affect the scaling behavior of the spin stiffness s and the magnetic response. Using a coherent spin-state path integral formulation and allowing for a non-uniform time varying external magnetic field we determine the dynamic susceptibility tensorχαβ. We find that stiffness and susceptibility satisfy a remarkable relation in the mesoscopic regime, viz. s/c2=χzz. We briefly discuss the experimental consequences of this relationship.