Page curve entanglement dynamics in an analytically solvable model

TL;DR

This paper presents an exactly solvable free fermion model demonstrating the Page curve of entanglement entropy in black hole physics, revealing a quantum phase transition and breakdown of semiclassical relations.

Contribution

It introduces a solvable fermion model that explicitly exhibits the Page curve and analyzes the associated quantum phase transition and entanglement dynamics.

Findings

Entanglement entropy follows the Page curve with a peak at the Page time.

Late-time entanglement entropy vanishes, indicating a breakdown of semiclassical relations.

Identifies a quantum phase transition in the entanglement Hamiltonian.

Abstract

The entanglement entropy of black holes is expected to follow the Page curve. After an initial linear increase with time the entanglement entropy should reach a maximum at the Page time and then decrease. This paper introduces an exactly solvable model of free fermions that explicitly shows such a Page curve: The entanglement entropy vanishes asymptotically for late times instead of saturating at a volume law. The bending down of the Page curve is accompanied by a breakdown of the semiclassical connection between particle current and entanglement generation, a quantum phase transition in the entanglement Hamiltonian and non-analytic behavior of the $q\rightarrow\infty$ Renyi entropy. These observations are expected to hold for a larger class of systems beyond the exactly solvable model analyzed here.