Global quantum discord in matrix product states and the application

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 (Gn) for consecutive n-site subsystems in infinite-size matrix product states (MPSs). We apply the method to study the scaling behavior of Gn 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-12 XXZ chain whose ground state is approximately expressed as MPSs with the help of infinite time-evolving block decimation (iTEBD) algorithm. In both models, as the increase of n, Gn shows an approximately linear growth. Unambiguous clue for the convergence of the incremental ΔGn=Gn−Gn−1 is observed when n is large enough. Moreover, in non-critical (gapped) regions ΔGn converges very fast, while in critical (gapless) regions it converges relatively slow. The behaviors are explained in a model-independent physical picture with finite-range correlations. Based on these results, we propose to use “discord per site” (Gnn) to describe the global correlations in infinite-size spin chains. Moreover, we find that the global discord shows a size-independent maximum at the infinite-order quantum phase transition point of the XXZ model.