魔法所构成之物：紧致算子代数、稳定器多面体以及Kitaev自旋液体中约化密度矩阵的结构

中文摘要 AI 辅助

量子多体系统展现出丰富而复杂的行为。“魔法”最近已成为探测这类系统的一种强大的新诊断工具，补充了多体纠缠等其他关键特征。本文从研究大型多体量子系统子系统内魔法的出现入手，表明出现了复杂结构，这些结构为揭示潜在的多体物理学提供了重要线索。聚焦于Kitaev蜂窝模型，我们首先确定了局部子系统开始获得魔法的温度。值得注意的是，我们发现在魔法出现时活跃的最优魔法见证算子揭示了紧致算子空间，这些空间在后续演化过程中仍能捕获局部热态。对于六位点六边形边际，这种关联可以更紧密：相同的算子空间独立于局部边际的对称性出现，并形成对称性分辨的 plaquette 代数（plaquette 即面元算子代数）。当这些对称性被精确实现时，局部态完全处于该代数内，且魔法的约化鲁棒性等于魔法的全鲁棒性。这种相同的约化描述也可应用于其他局部量子资源，我们用真正的多体纠缠对此进行了说明。此外，这些算子空间具有有限维欧几里得若当代数形式的丰富代数结构，可通过键和键循环算子进行自然解释。因此，我们的通用方法表明，局部魔法的出现如何揭示有限温度Kitaev自旋液体背后的紧致、具有物理意义的算子结构，并为多体系统中量子资源的约化描述开辟了新途径。

英文摘要

Quantum many-body systems exhibit rich and complex behaviour. Magic has recently emerged as a powerful new diagnostic for probing such systems, complementing other key features such as many-body entanglement. Here, starting from an investigation of the onset of magic within subsystems of a larger many-body quantum system, we show that intricate structures emerge which shed important light on the underlying many-body physics. Focusing on the Kitaev honeycomb model, we first identify the temperature below which local subsystems acquire magic. Remarkably, we find that the optimal magic witnesses active at the onset of magic reveal compact operator spaces that continue to capture the local thermal states throughout their subsequent evolution. For the six-site hexagonal marginal, this connection can be made stronger: the same operator space emerges independently from the symmetries of the local marginal and forms the symmetry-resolved plaquette algebra. When these symmetries are realized exactly, the local state lies entirely within this algebra and the reduced robustness of magic is equal to the full robustness of magic. The same reduced description can also be applied to other local quantum resources, which we illustrate using genuine multipartite entanglement. Furthermore, the operator spaces possess a rich algebraic structure in the form of finite-dimensional Euclidean Jordan algebras, with a natural interpretation in terms of bond and bond-cycle operators. Our general methodology therefore show how the onset of local magic can reveal a compact, physically meaningful operator structure underlying the finite-temperature Kitaev spin liquid, and opens up a new avenue towards reduced descriptions of quantum resources in many-body systems.

发表机构

• Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）
• University of Bristol（布里斯托大学）

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