Page curve entanglement dynamics in an analytically solvable model

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 $q\to \infty$ Renyi entropy. These observations are expected to hold for a larger class of systems beyond the exactly solvable model analyzed here.

12 pages, 12 figures. v3 is significantly revised from v2 and contains numerous new results, especially regarding non-analytic behavior of the min-entropy