# Correspondence between Entanglement Growth and Probability Distribution of Quasi-Particles

## TL;DR

This paper explores the relationship between entanglement entropy growth and quasi-particle probability distributions in free field theories, proposing a toy model that links entanglement excess to quasi-particle presence in subregions.

## Contribution

It establishes a correspondence between entanglement excess and quasi-particle probability distributions, introducing a toy model that reproduces this relationship in higher-dimensional free theories.

## Key findings

- Entanglement excess correlates with quasi-particle probability in subregions.
- A toy model successfully reproduces entanglement growth using free quasi-particle propagation.
- The framework applies to spacetime dimensions ≥ 4.

## Abstract

We study the excess of (Renyi) entanglement entropy in various free field theories for the locally excited states defined by acting with local operators on the ground state. It is defined by subtracting the entropy for the ground state from the one for the excited state. Here the spacetime dimension is greater than or equal to 4. We find a correspondence between entanglement and a probability. The probability with which a quasi-particle exists in a subregion gives the excess of the entropy. We also propose a toy model which reproduces the excess in the replica method. In this model, a quasi-particle created by a local operator propagates freely and its probability distribution gives the excess.