发表机构
International Center for Elementary Particle Physics, University of Tokyo（东京大学 elementary particle physics 国际中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Dyck-Fredkin自旋链基态的稳定化子Rényi熵，发现其标度依赖参数$t$：$t<1$时广延，$t=1$时对数，$t>1$时常数，为量子多体系统提供新视角。
AI 中文摘要
稳定化子Rényi熵是非稳定化子（即魔法）的定量度量，通常发现对于多种多体量子态，它随系统大小$N$呈广延标度（即$\Theta(N)$）。在本文中，我们研究了自旋-$\frac{1}{2}$ Dyck-Fredkin链及其$t$-形变（一种具有异常谱隙标度的局域无阻挫模型）基态的稳定化子Rényi熵。利用组合结构，我们进行了数值精确的有限尺寸计算，结果表明渐近行为依赖于$t$：对于$t<1$为$\Theta(N)$，在$t=1$时为$\Theta(\log N)$，对于$t>1$为$\Theta(1)$。在$t=1$处的标度可能是该模型非常规临界性的另一种表现，而与纠缠熵行为的对比表明，非稳定化子度量可能为量子多体系统提供新的视角。
英文摘要
The stabilizer Rényi entropy is a quantitative measure of non-stabilizerness, or magic, and has typically been found to scale extensively with system size $N$ (i.e., $Θ(N)$) for a variety of many-body quantum states. In this note, we study the stabilizer Rényi entropy of the ground state of the spin-$\frac{1}{2}$ Dyck-Fredkin chain and its $t$-deformation, a local frustration-free model with unusual spectral-gap scaling. Exploiting the combinatorial structure, we carry out numerically exact finite-size calculations, which indicate asymptotic behavior depending on $t$: $Θ(N)$ for $t<1$, $Θ(\log N)$ at $t=1$, and $Θ(1)$ for $t>1$. The scaling at $t=1$ could be another manifestation of the unconventional criticality of the model, while the contrast with the behavior of the entanglement entropy suggests that non-stabilizerness might provide a new window into quantum many-body systems.
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