Global quantum discord in matrix product states and the application

Abstract 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 block decimation (iTEBD) algorithm. In both models, as the increase of n , G n shows an approximately linear growth. Unambiguous clue for the convergence of the incremental Δ G n = G n − G n − 1 is observed when n is large enough. Moreover, in non-critical (gapped) regions Δ G n 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” ( G n n ) 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.