# Quantum Entanglement of Localized Excited States at Finite Temperature

**Authors:** Pawel Caputa, Joan Simon, Andrius Stikonas, Tadashi Takayanagi  
**arXiv:** [1410.2287](https://arxiv.org/abs/1410.2287)  
**Date:** 2014-10-08  
**Summary page:** https://www.summarizepaper.com/en/paper/1410.2287v2/

## Key points

- Authors: Pawel Caputa, Joan Simon, Andrius Stikonas, Tadashi Takayanagi
- Study focus: Quantum entanglement in two-dimensional conformal field theories (CFTs) at finite temperature
- Locally excited states created by applying local operators to thermal states
- Analysis through field theoretic and holographic calculations
- Reduction in growth of Renyi entanglement entropy at finite temperature in free field CFTs
- Entanglement entropy convergence towards characteristic value over time in finite temperature CFTs with classical gravity duals
- Exploration of mutual information between two CFTs within the thermofield double (TFD) formulation
- Contribution to understanding quantum entanglement dynamics and impact of thermal effects on entanglement properties in theoretical frameworks involving CFTs and holography

## Summary

In their work titled "Quantum Entanglement of Localized Excited States at Finite Temperature," authors Pawel Caputa, Joan Simon, Andrius Stikonas, and Tadashi Takayanagi delve into the intricate study of quantum entanglement in two-dimensional conformal field theories (CFTs) at finite temperature. They focus on locally excited states created by applying local operators to thermal states and provide a comprehensive analysis through both field theoretic and holographic calculations. Their findings reveal interesting insights into the behavior of Renyi entanglement entropy in different scenarios. In free field CFTs, they observe a reduction in the growth of Renyi entanglement entropy at finite temperature compared to its zero-temperature counterpart, attributed to a small quantity proportional to the width of localized excitations. In finite temperature CFTs with classical gravity duals, they discover that the entanglement entropy converges towards a characteristic value as time progresses, a phenomenon not observed at zero temperature. Additionally, the authors explore mutual information between two CFTs within the thermofield double (TFD) formulation and offer physical interpretations for their results. This study significantly contributes to our understanding of quantum entanglement dynamics in complex systems and sheds light on how thermal effects impact entanglement properties in theoretical frameworks involving CFTs and holography.