The holographic entanglement pattern of BTZ planar black hole from a thread perspective

TL;DR

This paper explores the detailed structure of quantum entanglement in a finite-temperature holographic setting using entanglement threads, revealing new insights into the entanglement contributions across the BTZ black hole horizon.

Contribution

It introduces a quantitative flux function for entanglement threads crossing the wormhole horizon, providing a more detailed characterization than previous bit thread approaches.

Findings

Derived the flux function of entanglement threads crossing the horizon

Linked entanglement threads to tensor network states and perfect entanglement

Connected the work to concepts like bit threads and partial entanglement entropy

Abstract

In this paper, we study the holographic quantum entanglement structure in the finite-temperature CFT state/planar BTZ black hole correspondence from the perspective of entanglement threads. Unlike previous studies based on bit threads, these entanglement threads provide a more detailed characterization of the contribution sources to the von Neumann entropy of boundary subregions, in particular by quantitatively deriving the flux function of entanglement threads that traverse the wormhole horizon and connect the two asymptotic boundaries. Since entanglement threads are naturally and closely related to tensor network states, the results are argued to imply the existence of the perfect-type entanglement formed jointly by the entanglement threads crossing the wormhole and the internal threads in the single-sided boundary. We also discuss the close connections of this work with concepts such as bit threads and partial entanglement entropy.