Replica Wormholes and Holographic Entanglement Negativity

TL;DR

This paper investigates the quantum entanglement structure of evaporating black holes using replica wormholes, revealing four geometric phases and phase transitions that deepen understanding of black hole evaporation.

Contribution

It introduces a detailed analysis of entanglement negativity in toy models, discovering new replica wormhole geometries and phase transitions in black hole entanglement structure.

Findings

Identifies four dominant geometric phases in black hole entanglement.

Discovers new replica wormholes that break replica symmetry.

Finds enhanced negativity corrections near phase transitions.

Abstract

Recent work has shown how to understand the Page curve of an evaporating black hole from replica wormholes. However, more detailed information about the structure of its quantum state is needed to fully understand the dynamics of black hole evaporation. Here we study entanglement negativity, an important measure of quantum entanglement in mixed states, in a couple of toy models of evaporating black holes. We find four phases dominated by different types of geometries: the disconnected, cyclically connected, anti-cyclically connected, and pairwise connected geometries. The last of these geometries are new replica wormholes that break the replica symmetry spontaneously. We also analyzed the transitions between these four phases by summing more generic replica geometries using a Schwinger-Dyson equation. In particular, we find enhanced corrections to various negativity measures near the transition between the cyclic and pairwise phase.