Revealing Entanglement-Growth Mechanisms through the Magic Barrier
Quantum entanglement and magic are complementary resources underlying quantum computational advantage, yet their dynamical relation in many-body systems remains poorly understood. In this Letter, we show that the mechanism of bipartite entanglement growth is encoded in the relative timescale between the entropy-growth-rate peak and the magic barrier, defined as the transient peak of the anti-flatness of the entanglement spectrum. When entanglement is locally built, the same microscopic process increases the entropy and reshapes the Schmidt spectrum, so the magic-barrier peak occurs in the time window of maximal entropy growth. When entanglement is mainly transported or redistributed, entropy can grow before appreciable spectral non-flatness is generated, naturally separating the two peak times. We demonstrate this distinction in the random-field XXZ chain: the two peaks remain strongly correlated in the thermal regime, while their separation grows systematically across the thermal--MBL crossover. We further validate this theoretical framework by employing Bell-pair initial states alongside a tunable SWAP--Haar random circuit. Our results reveal an intrinsic dynamical connection between entanglement and magic, establishing the magic barrier as a powerful spectral diagnostic of how quantum information is generated, transported, and reshaped.