Two-point correlators of modular Hamiltonians obey entropy-like properties and equal the stress-tensor conformal block for spherical regions in CFT, including imaginary-time separations.
Correlation function of modular Hamiltonians
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We investigate varies correlation functions of modular Hamiltonians defined with respect to spatial regions in quantum field theories. These correlation functions are divergent in general. We extract finite correlators by removing divergent terms for two dimensional massless free scalar theory. We reproduce the same correlators in general two dimensional conformal field theories.
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Correlation functions of von Neumann entropy
Two-point correlators of modular Hamiltonians obey entropy-like properties and equal the stress-tensor conformal block for spherical regions in CFT, including imaginary-time separations.