arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2408.04592quant-phcond-mat.str-el
收藏

拓扑纠缠熵不等式的物理证明

Physical proof of the topological entanglement entropy inequality

Michael Levin

备注：
11 pages, 6 figures; published version
发表信息：
Phys. Rev. B 110, 165154 (2024)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文利用冯·诺依曼熵的强次可加性和基态密度算符的物理假设，给出了拓扑纠缠熵不等式 $γ\geq \log \mathcal{D}$ 的更直接证明，并将其推广到非均匀、高维及混合态系统。

摘要：

最近有研究表明，二维有能隙基态的拓扑纠缠熵（TEE）满足普适不等式 $γ\geq \log \mathcal{D}$，其中 $γ$ 是 TEE，$\mathcal{D}$ 是所有任意子激发的总量子维度，$\mathcal{D} = \sqrt{\sum_a d_a^2}$。本文我们给出该不等式的另一种更直接的证明。我们的证明仅使用冯·诺依曼熵的强次可加性，以及对基态密度算符的若干物理假设。我们的推导自然推广到多种系统，包括具有缺陷和边界的空间非均匀系统、高维系统以及混合态。

英文摘要：

Recently it was shown that the topological entanglement entropy (TEE) of a two-dimensional gapped ground state obeys the universal inequality $γ\geq \log \mathcal{D}$, where $γ$ is the TEE and $\mathcal{D}$ is the total quantum dimension of all anyon excitations, $\mathcal{D} = \sqrt{\sum_a d_a^2}$. Here we present an alternative, more direct proof of this inequality. Our proof uses only the strong subadditivity property of the von Neumann entropy together with a few physical assumptions about the ground state density operator. Our derivation naturally generalizes to a variety of systems, including spatially inhomogeneous systems with defects and boundaries, higher dimensional systems, and mixed states.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑