Würzburg Seminar on Quantum Field Theory and Gravity

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 -> infinity Renyi
entropy. These observations are expected to hold for a larger class of systems beyond the exactly
solvable model analyzed in my talk.