加权Berry曲率与混合量子态的全局几何
Weighted Berry curvature and global geometry of mixed quantum states
- Uppsala University（乌普萨拉大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究混合量子态量子几何张量的虚部，证明其一般不构成全局U(1)联络曲率，并以两能级系统为例展示曲面积分对曲面选择的依赖及非2π整数倍的歧义。
AI中文摘要：
我们考察了文献[Phys. Rev. B 110, 035404 (2024)]中针对混合量子态提出的量子几何张量的几何解释，重点关注其虚部，该虚部与密度算符本征态的Berry曲率的加权和成正比。虽然实部自然分解为Fisher-Rao和加权Fubini-Study贡献，但我们证明，一般而言，虚部并不与全局定义的U(1)线丛上的联络曲率重合，该线丛的和乐给出混合态几何相位。以两能级系统为具体例子，我们证明其曲面积分依赖于由同一闭合路径所围成的曲面的选择，且歧义并非2π的整数倍。
英文摘要：
We examine the geometric interpretation of the quantum geometric tensor proposed in [Phys. Rev. B {\bf 110}, 035404 (2024)] for mixed quantum states, focusing on its imaginary part, which is proportional to a weighted sum of the Berry curvatures of the eigenstates of the density operator. While the real part naturally decomposes into Fisher--Rao and weighted Fubini--Study contributions, we show that the imaginary part does not, in general, coincide with the curvature of a connection on a globally defined U(1) line bundle whose holonomy yields a mixed-state geometric phase. Using a two-level system as an explicit example, we demonstrate that its surface integral depends on the choice of surface bounded by the same closed path, with ambiguities that are not integer multiples of $2π$.
