  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.
