The exact WKB analysis on correlation functions of low dimensional quantum systems and quantum entanglement.

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We develop a novel formulation in an exact quantitative study on the correlation functions of 1D quantum systems at finite temperature. This is accomplished by combining the quantum transfer method and the exact WKB method.The formulation enables us to carry a rigorous numerical study on the quantum correlations. As a concrete example, we apply it to the spin 1/2 quantum XXZ chain.The variety of behaviors of the correlation functions and quantum entanglement is observed as we change the system temperature and an applied magnetic field.