AI 中文总结
研究任意子-哈伯德模型中统计相位与格点相互作用的关系，确定量子多体伤疤本征态和淬火动力学，揭示Krylov复杂性的演化规律，明确统计相位对多体动力学的核心作用。
AI 中文摘要
任意子遵循介于玻色子和费米子统计之间的分数统计，产生了一系列引人入胜的现象。然而，任意子统计如何调控量子态复杂性仍在很大程度上未被探索。在这项工作中，我们研究了任意子-哈伯德模型中统计相位与格点相互作用之间的相互作用，确定了精确的量子多-body伤疤本征态和新颖的淬火动力学。在伤疤动力学中，Krylov复杂性表现出与统计相位无关的完美周期性复兴；而在淬火后，它同时依赖于统计相位和相互作用强度。在强相互作用区域，我们发现近似的伤疤动力学；在弱相互作用区域，态在Krylov空间中扩散，复杂性最终达到饱和。此外，对于玻色子初态，费米子的复杂性表现出最低的饱和值，反之亦然。对于分数统计，当淬火后的统计相位接近初态的统计相位时，饱和平台达到最小。我们的结果证明了统计相位在调控多体动力学中的核心作用，并为Krylov复杂性和量子多体伤疤提供了新的见解。
英文摘要
Anyons obey fractional statistics that lie between bosonic and fermionic statistics, giving rise to a broad range of intriguing phenomena. However, how anyonic statistics govern quantum-state complexity is still largely unexplored. In this work, we investigate the interplay between the statistical phase and on-site interactions in the anyon-Hubbard model, identifying exact quantum many-body scar eigenstates and novel quench dynamics. The Krylov complexity exhibits perfect periodic revivals independent of the statistical phase in the scarred dynamics, whereas after a quench it depends on both the statistical phase and the interaction strength. In the strong-interaction regime, we find approximate scarred dynamics, while in the weak-interaction regime the state spreads over Krylov space and the complexity ultimately saturates. Moreover, for the bosonic initial state, the complexity of fermions exhibits the lowest saturation value, and vice versa. For fractional statistics, the saturation plateau is minimized when the post-quench statistical phase is close to that of the initial state. Our results demonstrate the central role of the statistical phase in governing many-body dynamics and provide new insights into Krylov complexity and quantum many-body scars.
Comments8 pages, 6 figures
