# Instantons and Entanglement Entropy

## TL;DR

This paper investigates whether non-perturbative instanton effects alter the entanglement entropy's area law in various quantum field theories, finding that the law remains valid despite these effects.

## Contribution

It provides the first detailed analysis of instanton corrections to entanglement entropy across multiple models, confirming the robustness of the area law.

## Key findings

- Instanton effects do not violate the area law in studied models.
- Numerical results show superpositions of vacua behave similarly to single Fermi surfaces.
- The area law holds even with non-perturbative instanton corrections.

## Abstract

We would like to put the area law -- believed to by obeyed by entanglement entropies in the ground state of a local field theory -- to scrutiny in the presence of non-perturbative effects. We study instanton corrections to entanglement entropy in various models whose instanton effects are well understood, including $U(1)$ gauge theory in 2+1 dimensions and false vacuum decay in $\phi^4$ theory, and we demonstrate that the area law is indeed obeyed in these models. We also perform numerical computations for toy wavefunctions mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our results indicate that such superpositions exhibit no more violation of the area law than the logarithmic behavior of a single Fermi surface.