通过相互作用顶点关联表述的广义量子几何
Interacting quantum geometry from dressed parametric vertices
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中文总结 AI 辅助
将量子几何从布洛赫能带推广到包含集体玻色子涨落、外场或结构畸变等绝热参数流形，并证明广义量子几何张量由相互作用顶点关联编码。
中文摘要 AI 辅助
量子几何表征固体中电子波函数沿参数空间的变化。通常，晶体动量被选为参数，因为它与电磁场耦合，从而通过偶极矩阵元、极化涨落和光学响应来诠释量子几何。然而，布洛赫动量并非波函数演化的唯一可能参数空间。在这项工作中，我们证明量子几何可以扩展到裸布洛赫能带几何之外，到达绝热参数表示基态形变的流形，包括集体玻色子涨落、外场或结构畸变。我们证明广义量子几何张量由相互作用顶点关联编码，这些顶点与形变参数共轭。作为示例，我们简要讨论了这些扩展几何概念在由Hubbard-Stratonovich玻色子场或Jahn-Teller构型空间生成的流形上的应用。本文提出的表述以一般流形为框架，将量子几何推广到一般的结构、集体和相互作用多体系统。
英文摘要
Quantum geometry has emerged as a powerful framework for understanding topological, optical and transport phenomena, revealing connections between the quantum geometric tensor (QGT) and linear response functions. Building on these developments, recent works formulate quantum geometry so that the parameter space is extended from the Brillouin zone to the space of external perturbing fields that modify the ground state. Here we develop a self-consistent diagrammatric route to determine the QGT for generic parameter spaces, including collective fluctuations or structural distortions. With this in view, we generalize previous approaches to build the geometric tensor from interacting vertex correlations that provide the spectral metric and curvature. The formalism presented here extends the interaction-dressed vertex approach (previously applied to electromagnetic responses in momentum space) to collective electronic and structural deformation fields, complementing ongoing efforts to quantify many-body contributions to quantum geometry.
