Ising model. The analysis is performed either at zero or finite temperatures. For the case of zero-temperature, a quantum phase transition (QPT) is successfully characterized by the GQD measure. For finite temperatures, robustness against thermal fluctuations and its relationship with the transverse field is discussed.
In my opinion, the work seems correct and contains relevant results. Since multipartite correlations are expected to play an important role for the properties of many-body systems, I consider it is indeed interesting to see clear characterizations of QPTs and finite-temperature behaviors through GQD. So I recommend the publication. In order to promote some
improvements in the readability of the paper, I would like to suggest the Authors to address the following items:
i) In the introduction, the Author mentions that quantum discord exhibits remarkable properties concerning long-range decay. This is true, but it has been firstly pointed out in Ref. J. Maziero et al., Phys. Rev. A 82, 012106 (2010). I suggest to include
this reference in addition to the current Ref. [16] quoted.
Response: We thank the referee for bring us to the paper "Quantum and classical thermal correlations in the XY spin-1/2
chain, Phys. Rev. A 82, 012106 (2010)" by J. Maziero. We have cited this paper in the revised manuscript.
ii) In Section 2.1, the Author mentions that "… because of its operational interpretation, GQD can be used in quantum communication.". I suggest to add a reference to make this point stronger.
We have added two papers into the sentence. The first one is
"No-Local-Broadcasting Theorem for Multipartite Quantum Correlations, Phys. Rev. Lett. 100, 119903 (2008)" by Marco Piani. In addition, we find this paper when we read Liu's paper "Anna. Phys. 348 (2014) 256–269". Thereby we have also cited both papers in the revised manuscript.
iii) How is the 2D transverse-field Ising model solved in the infinite-size limit? The Author should improve the discussion in Section 3.2. It is clear the finite-size solution, but the limitations (if any) involved in the infinite case should be better discussed.submitting
The finite-size lattices are solved by the finite-size projected-entangled-pair-state (PEPS) algorithm.
The infinite-size lattices are solved by the infinite-size PEPS (iPEPS) algorithm. In both situations, we use the imaginary-time evolution method to figure out the ground state. The limitation of the iPEPS method is also added in Page 4 (add some sentences about the precision of the algorithm). According to the referee's comment, we have added some sentences in Sec. 3.1 about some details of the method.
iv) In Figure 3, after the QPT critical point, all the curves (for the various N) approximately coincide with each other. The
Author provides a brief explanation in terms of a little size effect. However, is there a more intuitive reason for the
approximate size independence after the QPT?
v) I agree with the Author that the robustness of GQD against temperature for high fields is indeed remarkable, as shown in Figs. 6c and 7c. However, curiously, since large strong fields tend to completely destroy the quantum correlations, how come do these large fields show more robustness as function of T? I think this point could be better discussed (and perhaps emphasized) in the text.
Indeed, the strong fields tend to completely destroy the quantum correlations, as illustrated in the sub-lattice discord in Fig. 3 and the entire-lattice discord in Fig. 4. The strength of the quantum correlations

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