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. 71.10.Fd Introduction. Tensor networks (TN) provide a convenient means to represent quantum wave functions in classical simulations of quantum many-body lattice systems, such as the matrix product states (MPS) [1][2][3][4][5] in one spatial dimension and the projected entangled-pair state (PEPS) [6][7][8] in two and higher spatial dimensions. The development of various numerical algorithms in the context of the TN representations has led to significant advances in our understanding of quantum many-body lattice systems in both one and two spatial dimensions [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Lying between quantum lattice systems in one and two spatial dimensions, spin ladders have attracted a lot of attention, due to their intriguing critical properties. Given the importance of spin ladder systems in condensed matter physics, it is somewhat surprising that no efforts have been made to develop any efficient algorithm in the context of the TN representations.This paper aims to fill in this gap. The algorithm generates efficiently ground-state wave functions for infinite-size spin ladders. In addition, it allows 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. In fact, as argued in Refs. [18][19][20][21][22][23], the ground-state fidelity per lattice site is able to capture drastic changes of the ground-state wave functions around a critical point. 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 [24,25] based on the density matrix renormalization group (DMRG) [26]. Our results indicate that the ground-state fidelity per lattice site successfully captures quantum criticalities in spin ladders.Tensor network representation for spin ladders. Let us describe the TN representation suitable to describe a groundstate wave function for an infinite-size spin ladder. Suppose the Hamiltonian is translationally invariant under shifts by either one or two lattice sites along the legs: H = i,α h i,α , with the i, α -th plaquette Hamiltonian density h i,α...
