Page curve and entanglement dynamics in an interacting fermionic chain

Generic nonequilibrium many-body systems display a linear growth of bipartite entanglement entropy in time, followed by a volume law saturation. In stark contrast, the Page curve dynamics of black-hole physics shows that the entropy peaks at the Page time <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>t</a:mi><a:mtext>Page</a:mtext></a:msub></a:math> and then decreases to zero. Here, we investigate such Page-like behavior of the von Neumann entropy in a model of strongly correlated spinless fermions in a typical system-environment setup and characterize the properties of the Page curve dynamics in the presence of interactions using numerically exact matrix product states methods. The two phases of growth, namely, linear growth and bending down, are shown to be separated by a nonanalyticity in the min-entropy before <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>t</b:mi><b:mtext>Page</b:mtext></b:msub></b:math>, which separates two different quantum phases, realized as the respective ground states of the corresponding entanglement (or equivalently, modular) Hamiltonian. We confirm and generalize, by introducing interactions, the findings of for a free spinless fermionic chain where the corresponding entanglement Hamiltonian undergoes a quantum phase transition at the point of nonanalyticity. However, in the presence of interactions, a scaling analysis gives a nonzero critical time for the nonanalyticity in the thermodynamic limit only for weak to intermediate interaction strengths, while the dynamics leading to the nonanalyticity becomes for interactions large enough. We present a physical picture explaining these findings.