We propose a static auxiliary field approximation to study the hybridization physics of Kondo systems without the sign problem and use the mutual information to measure the intersite hybridization correlations. Our method takes full account of the spatial fluctuations of the hybridization fields at all orders and overcomes the artificial (first-order) phase transition predicted in the mean-field approximation. When applied to the two-impurity Kondo model, it reveals a logarithmically divergent amplitude mutual information near the so-called Varma-Jones fixed point and a large phase mutual information manifesting the development of intersite phase coherence in the Kondo regime, with observable influences on physical properties. These highlight the importance of hybridization fluctuations and confirm the mutual information as a useful tool to explore the hybridization physics in Kondo systems.
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