Page curve dynamics in interacting fermionic chains

Generic non-equilibrium many-body systems display a linear growth of bipartite entanglement entropy in time followed by a volume law saturation. We present a new class of models that display a linear growth followed by bending down of the entanglement, instead of saturation, all the way down to zero. This entanglement dynamics is already known in the field of black hole physics as the Page curve where the peak value is obtained at what is known as the Page time. We show that the two phases of growth in our non-equilibrium condensed matter system, namely the linear growth and the bending down, is separated by a non-analyticity in the min-entropy before the Page time, thereby leading to two different quantum phases of matter. This can be shown in the thermodynamic limit for a free spinless fermionic chain where the entanglement Hamiltonian undergoes a quantum phase transition at the point of non-analyticity. We further show the persistence of the behaviors, namely the Page curve as well as the non-analyticity of the min-entropy before the Page time, even when we switch on the interactions in the fermionic chain.