Kinematic Emergence of the Page Curve in a Local Transverse-Field Ising Model

We present a controllable quantum spin-chain model that reproduces the Page curve (the rise-and-fall of bipartite entanglement expected in black-hole evaporation), using only local interactions and a kinematic reduction of the subsystem size. Two transverse-field Ising chains are coupled to form a pure bipartite state; Hawking-like evaporation is implemented by dynamically shrinking the 'system' chain and enlarging the 'environment' chain, while unitary real-time evolution is simulated with matrix product state (MPS) tensor networks. The characteristic Page curve profile emerges robustly under this controlled subsystem resizing and notably persists even when the explicit Hamiltonian coupling across the boundary is set to zero, demonstrating that shrinking Hilbert-space dimension alone can generate Page curve behaviour. We show that the detailed shape of the curve depends on the internal information dynamics: operation at criticality yields a smooth profile, whereas moving away from criticality distorts entanglement growth and decay. These results position locally interacting spin chains as a realistic platform for probing black-hole-inspired information dynamics on current quantum hardware.