Spin Stiffness of Mesoscopic Quantum Antiferromagnets

We study the spin stiffness of a one-dimensional quantum antiferromagnet in the whole range of system sizes $L$ and temperatures $T$. We show that for integer and half-odd integer spin cases the stiffness differs fundamentally in its $L$ and $T$ dependences, and that in the latter case the stiffness exhibits a striking dependence on the parity of the number of sites. Integer spin chains are treated in terms of the nonlinear sigma model, while half-odd integer spin chains are discussed in a renormalization group approach leading to a Luttinger liquid with Aharonov-Bohm-type boundary conditions.