We study the finite size scaling of the spin stiffness for the
one-dimensional s=1/2 quantum antiferromagnet as a function of the anisotropy
parameter Delta.Previous Bethe ansatz results allow a determination of the
stiffness in the thermodynamic limit. The Bethe ansatz equations for finite
systems are solvable even in the presence of twisted boundary conditions, a
fact we exploit to determine the stiffness exactly for finite systems allowing
for a complete determination of the finite size corrections. Relating the
stiffness to thermodynamic quantities we calculate the temperature dependence
of the susceptibility and its finite size corrections at T=0. A Luttinger
liquid approach is used to study the finite size corrections using
renormalization group techniques and the results are compared to the
numerically exact results obtained using the Bethe ansatz equations. Both
irrelevant and marginally irrelevant cases are considered
