Stiffness in 1D Matrix Product States with periodic boundary conditions

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.