Page Curve Like Entanglement Dynamics in Many-Body Quantum Systems: A Study of a Free Fermionic Model

Abstract

This thesis investigates entanglement dynamics in open quantum many-body systems, focusing on a one-dimensional free-fermion model in which a finite system is coupled to a large environment. We study the model introduced in Ref. [1], which becomes exactly solvable in the weak-coupling limit. Using resonant-level-model factorization, we derive analytical expressions for the entanglement dynamics and validate them with numerical simulations based on the correlation matrix formalism. We show that the system exhibits Page-curve-like behavior: the entanglement entropy grows at early times, reaches a maximum at the Page time (proportional to system size), and then decreases at late times. In the appropriate scaling regime, data for different system sizes collapse onto a single curve when plotted against the emitted-particle fraction. These results provide an analytically controlled and numerically validated framework for understanding Page-curve dynamics in open free-fermion systems.