受挫四面体上的热纠缠：通过并发度和稳定子结构探测量子资源
Thermal entanglement on a frustrated tetrahedron: Probing quantum resources through concurrence and stabilizer structure
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中文总结 AI 辅助
本研究通过线性优化和并发度上界，分析四面体受挫自旋系统的热纠缠，发现可分离热态区域，并用稳定子Rényi诊断探索量子魔力，为量子资源研究提供实用基础。
中文摘要 AI 辅助
在受挫自旋系统中，高度纠缠的本征态可以形成可分离的热混合态。我们针对热四面体（烧绿石晶格的基本单元）上的四个自旋-1/2 矩，在一般四参数交换哈密顿量下研究了这一区别。四面体对称性允许通过线性优化对热态分解进行受限搜索，从而得到多体并发度的上界，以及在该上界为零时的显式可分离分解。在低温下，并发度图显示在全进全出极限附近存在扩展的可分离区域，而在自旋冰点附近的抑制则狭窄地局域化。加热会因邻近多重态的重新布居而拓宽后一区域。优化识别出完全可分离的热态，即使本征态平均并发度仍然很大。负性独立地确认了选定耦合区域中的有限温度纠缠。一种混合态稳定子Rényi诊断（用于探索量子魔力）偏好不同的耦合，并且可能随温度局部增加。这些结果将热纠缠与对称性多重态的劈裂和布居联系起来，并为识别超出基态极限的量子资源研究的受挫自旋构型提供了实用基础。
英文摘要
In a frustrated spin system, highly entangled eigenstates can form a separable thermal mixture. We study this distinction for four spin-$1/2$ moments on a tetrahedron, the elementary unit of the pyrochlore lattice, with the general four-parameter exchange Hamiltonian. Tetrahedral symmetry allows a restricted search over thermal-state decompositions to be carried out by linear optimization, yielding an upper bound on multipartite concurrence and explicit separable decompositions where this bound vanishes. At low temperature, the concurrence maps show extended separable regions near the all-in--all-out limit, whereas suppression near the spin-ice point is narrowly localized. Heating broadens the latter region as nearby multiplets are repopulated. The optimization identifies fully separable thermal states even when the eigenstate-averaged concurrence remains large. Negativity independently confirms finite-temperature entanglement in selected coupling regions. A mixed-state stabilizer Rényi diagnostic, used to explore quantum magic, favours different couplings and can increase locally with temperature. These results connect thermal entanglement to the splitting and population of symmetry multiplets, and provide a practical basis for identifying frustrated spin configurations for studies of quantum resources beyond the ground-state limit.
发表机构
- Memorial University of Newfoundland（纽芬兰纪念大学）
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