Stiffness in 1D matrix product states with periodic boundary conditions

We discuss in detail a modified variational matrix product state algorithm for periodic boundary conditions, based on a recent work by Pippan et al (2010 Phys. Rev. B 81 081103(R)), which enables one to study large systems on a ring (composed of N ~ 100 sites). In particular, we introduce a couple of improvements allowing us to enhance the algorithm in terms of stability and reliability. We employ such a 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.