AI 中文总结
研究Kramers-Wannier对偶在非平衡态的情况，引入纠缠不对称性来量化其对称破缺。通过研究平衡性质和量子猝灭，发现了量子Mpemba效应，提供了相关证据并确定机制，为非平衡态非可逆对称研究及量子多体系统对偶性动力学带来新视角。
AI 中文摘要
Kramers-Wannier对偶是非可逆对称的典型例子，但对其远离临界点和非平衡态的情况知之甚少。我们引入了Kramers-Wannier纠缠不对称性，这是一种量子信息度量，用于量化横向场伊辛链中这种非可逆对称的破缺。首先研究其平衡性质，发现它在有序和无序相之间呈现显著交叉，在临界点有明显凹陷且随子系统大小变尖锐。接着研究从带隙相到临界点的量子猝灭，表明该不对称性衰减至零，意味着非可逆对称的动态恢复。还发现了量子Mpemba效应：在合适条件下，初始远离平衡的态比更接近平衡的态更快恢复Kramers-Wannier对称。我们提供了分析和数值证据并确定了其发生机制。这项工作将纠缠不对称性确立为非平衡态下非可逆对称的有力探针，为量子多体系统中对偶性的动力学开辟了新视角。
英文摘要
The Kramers-Wannier duality is the prototypical example of a non-invertible symmetry, yet little is known about its fate away from criticality and out of equilibrium. We introduce the Kramers-Wannier entanglement asymmetry, a quantum-information measure that quantifies the breaking of this non-invertible symmetry in the transverse-field Ising chain. We first investigate its equilibrium properties, showing that it exhibits a striking crossover between the ordered and disordered phases together with a pronounced dip at the critical point that becomes increasingly sharp with subsystem size. We then study quantum quenches from both gapped phases to criticality and show that the Kramers-Wannier entanglement asymmetry decays to zero, signaling the dynamical restoration of the non-invertible symmetry. Remarkably, we uncover the emergence of a quantum Mpemba effect: under suitable conditions, states initially farther from equilibrium restore the Kramers-Wannier symmetry faster than states prepared closer to it. We provide both analytical and numerical evidence for this phenomenon and identify the mechanism responsible for its occurrence. Our work establishes entanglement asymmetry as a powerful probe of non-invertible symmetries beyond equilibrium and opens new perspectives on the dynamics of dualities in quantum many-body systems.
Comments27 pages, 5 figures
