发表机构
UC Berkeley（加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用复 Perron-Frobenius 理论给出 Lee-Yang 张量的几何描述，推广关键引理以界定非正规算子谱比，并证明 Suzuki-Fisher 哈密顿量是唯一在所有逆温度下吉布斯态具有 Lee-Yang 性质的哈密顿量。
AI 中文摘要
我们基于 Bravyi、Gosset、Liu 和 Wong 的几项近期成果，对 Lee-Yang 张量给出了几何描述。通过应用复 Perron-Frobenius 理论中的工具，我们推广了他们的一项关键引理，以界定具有大于 1 的 Lee-Yang 半径的非正规算子的谱比。作为直接推论，我们提供了一个局部到整体的原理，用于界定 Suzuki-Fisher 哈密顿量（一族 2-局域哈密顿量）的谱隙，仅使用每个局域算子的 Lee-Yang 半径来从下方界定该隙。另一方面，我们发展了一种简单的微扰技术，以证明 $k$-局域哈密顿量（$k \geq 3$）的吉布斯态不可能对所有逆温度 $\beta \geq 0$ 具有至少为 1 的 Lee-Yang 半径。我们应用同一方法得出结论：Suzuki-Fisher 哈密顿量正是那些其吉布斯态在所有逆温度 $\beta \geq 0$ 下都是 Lee-Yang 的哈密顿量。
英文摘要
We provide a geometric description of Lee-Yang tensors, building upon several recent results of Bravyi, Gosset, Liu, and Wong. By applying tools from complex Perron-Frobenius theory, we generalize one of their key lemmas to bound the spectral ratio of non-normal operators with Lee-Yang radius greater than one. As a direct consequence, we provide a local-to-global principle for bounding spectral gaps of Suzuki-Fisher Hamiltonians, a family of $2$-local Hamiltonians, using only the Lee-Yang radius of each local operator to bound the gap from below. On the other hand, we develop a simple perturbative technique to show that the Gibbs states of $k$-local Hamiltonians, $k \geq 3$, cannot have Lee-Yang radius at least one for all inverse temperatures $β\geq 0$. We apply this same method to conclude that Suzuki-Fisher Hamiltonians are precisely those Hamiltonians whose Gibbs states are Lee-Yang at all inverse temperatures $β\geq 0$.
Comments43 pages, 1 figure
