  We have developed an efficient tensor network algorithm for spin ladders,
which generates ground-state wave functions for infinite-size quantum spin
ladders. The algorithm is able to efficiently compute the ground-state fidelity
per lattice site, a universal phase transition marker, thus offering a powerful
tool to unveil quantum many-body physics underlying spin ladders. To illustrate
our scheme, we consider the two-leg and three-leg Heisenberg spin ladders with
staggering dimerization. The ground-state phase diagram thus yielded is
reliable, compared with the previous studies based on the density matrix
renormalization group. Our results indicate that the ground-state fidelity per
lattice site successfully captures quantum criticalities in spin ladders.
