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Critical behaviors of mutual information in the one-dimensional spin-1 bilinear biquadratic model

The critical behaviors of the mutual information in the one-dimensional spin-1 bilinear biquadratic model are studied. It is found that all the quantum phase transition points including the order–disorder ones and the infinite-order ones in the system can be quantified from the singularity analysis of the mutual information of two sites with the longest distance, because the mutual information captures the correlation properties about the critical fluctuations. More interestingly, the special structure of the wavefunction and the special symmetric property of the system can be indicated by the entropy correlation behaviors. The finite size scaling laws of the mutual information and its derivative are also studied.