Correlation functions of von Neumann entropy

TL;DR

This paper investigates two-point correlation functions of modular Hamiltonians in quantum systems and conformal field theories, revealing their properties and connections to stress-tensor conformal blocks, with implications for holography.

Contribution

It provides a detailed analysis of modular Hamiltonian correlators, including explicit computations and exploration of their properties in various regimes, advancing understanding in quantum and conformal field theories.

Findings

Correlation functions obey properties similar to von Neumann entropy and entanglement capacity.

Explicit computation confirms the correlator's equivalence to stress-tensor conformal blocks.

Analysis across different regimes enhances understanding of modular Hamiltonian correlations.

Abstract

In this note, we study two-point correlation functions of modular Hamiltonians. We show that in general quantum systems, these correlators obey properties similar to those of von Neumann entropy and capacity of entanglement, both of which are special cases of these correlators. Then we specialize to two spacelike-separated spherical subregions in conformal field theories. We present direct computations of the vacuum two-point function that confirm its equivalence to the stress-tensor conformal block. We explore the two-point function in various kinematic regimes, including imaginary time separation between subsystems. The material presented in this note may be useful for further studying modular Hamiltonian correlators in generic quantum systems and in conformal field theories, including those with holographic duals.