发表机构
University of Geneva; Vrije Universiteit Brussel (VUB); RIKEN Centre for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（日内瓦大学; 布鲁塞尔自由大学; 理化学研究所跨学科理论与数学科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明单个局域缺陷足以在可积量子多体系统中生成近似酉k-设计，通过双泡利踢协议和解析选择规则，在混沌区域找到有效踢，且机制对弱缺陷随系统增大仍有效。
AI 中文摘要
我们证明，一个 $O(1)$ 的局域缺陷足以从原本可积的量子多体系统中生成近似酉 $k$-设计。利用带时间采样的双泡利踢（2PK）协议，我们在具有单一破可积性体缺陷的确定性 XXZ 自旋链的固定磁化扇区中演示了这一机制。我们推导出泡利踢的解析选择规则，并表明由耦合常数确定的具有特定畴壁数的对称保持弦支配着设计的形成。对所有可容许泡利弦的穷举搜索发现，在混沌区域中有一大类踢能产生设计，而在可积极限下（包括边界缺陷）则不存在此类踢。我们进一步表明，随着系统尺寸增大，该设计形成机制对弱体缺陷仍然有效。
英文摘要
We show that an $O(1)$ local defect is sufficient to generate approximate unitary $k$-designs from an otherwise integrable quantum many-body system. Using a two-Pauli-kick (2PK) protocol with temporal sampling, we demonstrate this mechanism in a fixed-magnetization sector of deterministic XXZ spin chains with a single integrability-breaking bulk defect. We derive an analytical selection rule for the Pauli kicks and show that symmetry-preserving strings with a specific domain-wall count, fixed by the couplings, govern design formation. An exhaustive search over all admissible Pauli strings identifies a broad family of kicks that produce designs in the chaotic regime, whereas no such kicks exist in the integrable limit, including for boundary defects. We further show that the design-forming mechanism remains effective for weak bulk defects as the system size increases.
Commentsv1: 15 pages total, 9 figures
