Scaling of entanglement entropy and hyperbolic geometry

TL;DR

This paper reviews how entanglement entropy scales in quantum systems, highlighting its connection to hyperbolic geometry and its role in linking quantum and classical systems, with implications for bulk/edge correspondence.

Contribution

It emphasizes the importance of entanglement entropy scaling in understanding the relationship between quantum systems, hyperbolic geometry, and classical counterparts, offering new insights into their mathematical similarities.

Findings

Scaling relations of entanglement entropy are crucial for system identification.

Hyperbolic geometry underpins the mathematical formulation of entanglement scaling.

Connections between bulk/edge correspondence and compactification are discussed.

Abstract

Various scaling relations of the entanglement entropy are reviewed. Based on the scaling, I would like to point out similarity of mathematical formulation among recent topics in wide research area. In particular, the scaling plays crucial roles on identifying a quantum system with a physically different classical system. Close connection between the scaling and hyperbolic geometry and contrast between bulk/edge correspondence and compactification for the identification are also addressed.