Mutual information and the structure of entanglement in quantum field theory

TL;DR

This paper investigates the structure of entanglement in scale-invariant quantum field theories using mutual information, revealing universal features and proposing a new computational approach with implications for holography and many-body physics.

Contribution

It introduces a novel method for computing entanglement measures in quantum field theories using higher-dimensional twist operators, highlighting universal entanglement features.

Findings

Mutual information remains finite in the continuum limit, providing a refined entanglement probe.

Universal singularities in mutual information reflect 'entanglement per scale'.

Proposes a new ansatz for calculating entanglement entropy and mutual information.

Abstract

I study the mutual information between spatial subsystems in a variety of scale invariant quantum field theories. While it is derived from the bare entanglement entropy, the mutual information offers a more refined probe of the entanglement structure of quantum field theories because it remains finite in the continuum limit. I argue that the mutual information has certain universal singularities that are a manifestation of the idea of "entanglement per scale". Moreover, I propose a method, based on an ansatz for higher dimensional twist operators, to compute the entanglement entropy, Renyi entropy, and mutual information in a general quantum field theory. The relevance of these results to the search for renormalization group monotones, to holographic duality, and to entanglement based simulation methods for many body systems are all discussed.