# Boundary effects in entanglement entropy

**Authors:** Clement Berthiere, Sergey N. Solodukhin  
**arXiv:** [1604.07571](https://arxiv.org/abs/1604.07571)  
**Date:** 2016-04-26  
**Summary page:** https://www.summarizepaper.com/en/paper/1604.07571v2/

## Key points

- Authors Clement Berthiere and Sergey N. Solodukhin focus on Renyi and entanglement entropies in $d$-dimensional Minkowski spacetime
- Study examines impact of boundary conditions when entangling surface intersects a boundary
- Observes breaking of translational symmetry along the entangling surface due to boundaries, leading to non-homogeneous distribution of entanglement
- Introduces density of entanglement entropy to quantify phenomenon, revealing maximal entanglement near the boundary
- Investigates scenarios with two parallel planes as boundaries, finding total contribution to entropy remains constant at twice that for single plane configuration
- Explores how changes in separation size between dual boundaries affect area law and its influence on UV finite parts of entropy calculations

## Summary

In their paper "Boundary effects in entanglement entropy," authors Clement Berthiere and Sergey N. Solodukhin delve into explicit calculations of Renyi and entanglement entropies within the context of $d$-dimensional Minkowski spacetime. They specifically focus on scenarios where the entangling surface intersects a boundary and examine the impact of various boundary conditions on entropy. The study also explores the flow in boundary coupling between different phases across arbitrary dimensions, highlighting peculiarities observed in the $d=3$ case. One key observation made by the authors is the breaking of translational symmetry along the entangling surface due to boundaries, resulting in non-homogeneous distribution of entanglement. To quantify this phenomenon, they introduce a density of entanglement entropy and provide explicit computations that reveal maximal entanglement near the boundary. The research also investigates scenarios where boundaries consist of two parallel planes separated by a finite distance. In these cases, both total entanglement entropy and its density are computed. The findings indicate that regardless of inter-plane distance, the total contribution to entropy from boundaries remains constant at twice that observed for a single plane configuration. Additionally, insights are offered on how changes in separation size between dual boundaries affect the area law – a component of entropy proportional to the entire surface area – showcasing its influence on UV finite parts of entropy calculations. Overall, Berthiere and Solodukhin's study sheds light on intricate boundary effects in entanglement entropy calculations. It offers valuable insights into non-uniform distribution patterns and contributions from distinct boundary configurations within diverse dimensional settings.