发表机构
South China Normal University（华南师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用最小相对非局域魔法研究随机场XXZ链的遍历性到多体局域化交叉，揭示施密特谱重组，并建立两能级模型解释其衰减，提供遍历性破缺的互补探针。
AI 中文摘要
非局域魔法量化了在两个子系统上独立局域幺正变换下可获得的最小非稳定子性。这里，我们使用最小相对非局域魔法（NLM）来表征随机场XXZ链中从遍历性到多体局域化（MBL）的交叉。与纠缠熵不同，NLM通过施密特谱与二进平坦稳定子谱的距离来探测纠缠的组织方式。从弱到中等无序，NLM从O(1)的Haar类值演变为尺寸增强的穹顶，而纠缠保持体积律，揭示了熵中不可见的谱重组。深入MBL区域，一个两能级切割杂化模型捕获了近二进施密特谱，并解释了为什么平均和中位数NLM分别近似按W^{-1}和W^{-2}衰减。在乘积态淬火后，NLM在遍历区域过冲并弛豫，而在强无序下它缓慢且近似对数增长。这些结果表明，NLM解析了纠缠熵中不可见的施密特谱结构，并提供了遍历性破缺的互补探针。
英文摘要
Nonlocal magic quantifies the minimum nonstabilizerness attainable under independent local unitary transformations on the two subsystems. Here, we use min-relative nonlocal magic (NLM) to characterize the crossover from ergodicity to many-body localization (MBL) in the random-field XXZ chain. Unlike entanglement entropy, NLM probes how entanglement is organized through the distance of the Schmidt spectrum from dyadic-flat stabilizer spectra. From weak to intermediate disorder, NLM evolves from an $O(1)$ Haar-like value into a size-enhanced dome, while entanglement remains volume-law, revealing a spectral reorganization not visible in the entropy. Deep in the MBL regime, a two-level cut-hybridization model captures the nearly binary Schmidt spectrum and explains why the mean and median NLM decay approximately as $W^{-1}$ and $W^{-2}$, respectively. Following a product-state quench, NLM overshoots and relaxes in the ergodic regime, whereas at strong disorder it grows slowly and approximately logarithmically. These results show that NLM resolves Schmidt-spectrum structure not visible in the entanglement entropy and provides a complementary probe of ergodicity breaking.
Comments6+9.5 pages,5+4 figures
