Relationship between susceptibility and spin stiffness of mesoscopic quantum antiferromagnets

We investigate the quantum antiferromagnetic Heisenberg spin chain of integer spin S in the semiclassical limit (S much greater than 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 rho(s) and the magnetic response. Using a coherent spin-state path integral formulation and allowing far a non-uniform time varying external magnetic field we determine the dynamic susceptibility tensor chi(alpha beta). We find that stiffness and susceptibility satisfy a remarkable relation in the mesoscopic regime, viz. rho(s)/c(2) = chi(zz). We briefly discuss the experimental consequences of this relationship.