AI 中文总结
研究量子纠缠和魔性在多体系统中的动力学关系，通过熵增长率峰值与魔障的相对时间尺度揭示二分纠缠增长机制，在随机场XXZ链中验证，并用特定电路进一步验证，确立魔障为量子信息相关的谱诊断工具。
AI 中文摘要
量子纠缠和魔性是量子计算优势背后的互补资源，然而它们在多体系统中的动力学关系仍知之甚少。在本论文中，我们表明二分纠缠增长机制编码于熵增长率峰值与魔障（定义为纠缠谱反平坦度的瞬态峰值）之间的相对时间尺度。当纠缠局部建立时，同一微观过程增加熵并重塑施密特谱，因此魔障峰值出现在最大熵增长的时间窗口。当纠缠主要是传输或重新分布时，熵可在可观的谱非平坦度产生之前增长，自然地分离两个峰值时间。我们在随机场XXZ链中证明了这种区别：在热态下两个峰值紧密相关，而在热态到多体局域化转变过程中它们的分离系统性增加。我们还通过使用贝尔对初始态以及可调SWAP - 哈尔随机电路进一步验证了该理论框架。我们的结果揭示了纠缠与魔性之间的内在动力学联系，确立了魔障作为量子信息如何产生、传输和重塑的强大谱诊断工具。
英文摘要
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.
