发表机构
The Abdus Salam ICTP; INFN, Sezione di Trieste; Rudolf Peierls Centre for Theoretical Physics, University of Oxford（阿卜杜斯·萨拉姆国际理论物理中心; 意大利国家核物理研究所的里雅斯特分部; 牛津大学鲁道夫·皮尔斯理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过直接数值实现迭代Schrieffer-Wolff构造，研究无序量子链中稀有非共振区域，验证了支撑次扩散输运的指数稀有长非共振区域的可求和性机制，并展示了数值方法对构造性证明的独立检验价值。
AI 中文摘要
我们通过直接实现De Roeck、Giacomin、Huveneers和Prosniak近期关于次扩散输运工作中所依据的迭代Schrieffer-Wolff构造，研究了一维无序量子自旋链这一典型模型中的稀有非共振区域。对于有限系统，我们计算了无序实现通过流动的连续尺度保持非共振的概率，同时分别监测算符增殖和缀饰局域可观测量的空间局域化。在数值可及的范围内，生存概率随系统尺寸最多呈指数衰减。逐尺度解析该衰减得到与连续Schrieffer-Wolff步骤相关的失败率。第一步的比率通过解析方法获得，与数值结果高度一致，而更高尺度的比率在研究范围内迅速减小。这些结果支持了指数稀有但参数上较长的非共振区域所需的可求和性机制，这些区域构成了导致次扩散输运的绝缘瓶颈。在我们研究的的最小耦合下，我们的条件下的生存概率超过严格下界六到七个数量级，这表明证明所需的常数是多么保守，同时证实其潜在物理机制在可及尺度上定量可见。更广泛地说，我们的结果展示了直接数值实现如何为技术要求高的构造性证明提供独立且物理透明的检验，这一方法随着机器辅助证明的日益普遍可能变得越来越有用。
英文摘要
We study rare nonresonant regions in a canonical one-dimensional disordered quantum spin chain by directly implementing the iterated Schrieffer-Wolff construction underlying the recent work of De Roeck, Giacomin, Huveneers and Prosniak on subdiffusive transport. For finite systems, we compute the probability that a disorder realization remains nonresonant through successive scales of the flow, while separately monitoring operator proliferation and the spatial localization of dressed local observables. The survival probability decays at most exponentially with system size over the numerically accessible regime. Resolving this decay scale by scale yields failure rates associated with successive Schrieffer-Wolff steps. The first rate is obtained analytically in excellent agreement with numerics, while higher-scale rates decrease rapidly throughout the regime studied. These results support the summability mechanism required for exponentially rare but parametrically long nonresonant regions, which provide the insulating bottlenecks responsible for subdiffusive transport. At the smallest couplings studied, the survival probability under our conditions exceeds the rigorous lower bound by six to seven orders of magnitude, demonstrating how conservative the constants required by the proof are while confirming that its underlying physical mechanism is quantitatively visible at accessible scales. More broadly, our results show how direct numerical implementations can provide an independent and physically transparent test of technically demanding constructive proofs, a methodology that may become increasingly useful as machine-assisted proofs become more common.
Comments30 pages, 5 figures
