Global quantum discord and thermal tensor network in XXZ chains at finite temperatures

We characterize multi-site quantum correlations in 1D finite-size XXZ chains at finite temperatures with global quantum discord. With the help of an exact diagonalization method and a thermal-tensor-network algorithm, the thermal-state discord G(ρˆT) is evaluated efficiently by well-developed optimization algorithms. Firstly, we find that in a finite temperature region, G(ρˆT) shows some footprint of the quantum phase transition of the model. The underlying mechanism is that ρˆT captures the level crossing in the low-lying excited states. Secondly, we study the temperature dependence of G(ρˆT). When the anisotropy is strong, G(ρˆT) will show a broad thermal plateau. We offer a quantitative explanation of the plateau by truncating the thermal-state operator ρˆT with respect to several low-lying states. Thirdly, we investigate the scaling behavior of G(ρˆT). We find that when N is large enough, G(ρˆT) would show a linear scaling. Finally, combined with the thermal tensor networks and the linear scaling behavior, we successfully figure out reliable results for G(ρˆT) in the full-temperature regions with N up to 16. We believe that the thermal tensor networks will play a role in studying general multi-site quantum correlations in 1D chains at finite temperatures.