Global quantum discord (GQD) is a measure of quantum correlation for multi-site quantum states. In this paper, we propose an efficient procedure to calculate global quantum discord (G(n)) for consecutive n-site subsystems in infinite-size matrix product states (MPSs). We apply the method to study the scaling behavior of G(n) in several one-dimensional infinite quantum spin chains, i.e., (1) a three-site interaction model whose ground state can be exactly expressed as MPSs, and (2) a spin-1/2 XXZ chain whose ground state is approximately expressed as MPSs with the help of infinite time-evolving...
