Boundary chaos: Exact entanglement dynamics

We compute the dynamics of entanglement in minimal setup producing ergodic and mixing quantum many-body dynamics, which we previously dubbed boundary chaos. This consists a free, non-interacting brickwork circuit, chaos ergodicity is induced by an impurity interaction, i.e., entangling two-qudit gate, placed at system’s boundary. both conventional bipartite entropy with respect to connected subsystem including interaction for initial product states as well so-called operator local operators. Thereby provide exact results particular scaling limit time system size going infinity either very small or large subsystems. show that different classes interactions lead distinct dynamics. For gates preserving state forming bulk state, entropies persistent spikes period set suppressed between, contrary expected linear growth systems. observe similar generic impurities. In contrast, T-dual impurities, remain unitary under partial transposition, find operators grow linearly maximum possible speed allowed geometry system. The intensive nature all cases causes on extensive scales proportional size.