# Correlation function of modular Hamiltonians

## TL;DR

This paper studies the correlation functions of modular Hamiltonians in quantum field theories, focusing on their divergences and finite parts, with explicit calculations in two-dimensional free scalar and conformal field theories.

## Contribution

It introduces a method to extract finite correlation functions of modular Hamiltonians by removing divergences, applicable to 2D free scalar and conformal field theories.

## Key findings

- Finite correlators are obtained after divergence removal.
- The method reproduces results in 2D conformal field theories.
- Divergences are characterized and systematically subtracted.

## Abstract

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.