  We discuss in details a modified variational matrix-product-state algorithm
for periodic boundary conditions, based on a recent work by P. Pippan, S.R.
White and H.G. Everts, Phys. Rev. B 81, 081103(R) (2010), which enables one to
study large systems on a ring (composed of N ~ 10^2 sites). In particular, we
introduce a couple of improvements that allow to enhance the algorithm in terms
of stability and reliability. We employ such method to compute the stiffness of
one-dimensional strongly correlated quantum lattice systems. The accuracy of
our calculations is tested in the exactly solvable spin-1/2 Heisenberg chain.
