哥伦比亚大学Raquel Queiroz团队的一项最新研究提出了绝缘体的瞬时响应和量子几何。2025年12月4日出版的《美国科学院院刊》杂志发表了这项成果。

研究人员提出了时间相关的量子几何张量（tQGT）作为一个综合的工具来捕捉在线性响应中可观察到的绝缘子的几何特征。课题组人员证明了tQGT描述了束缚电子的零点运动，并作为电子电导率广义和规则的生成函数。因此，它为计算绝缘体的瞬时响应提供了一个系统的框架，包括光学质量、轨道角动量和介电常数。这种结构保证了在限制无限大量子系统的低能量描述中占据和未占据状态的数量时，这些量之间的一致近似。研究人员概述了如何通过晶格干涉在周期系统中产生量子几何，并通过创建几何上的发光平坦带来检查从小频率到高频的谱权转移。

附：英文原文

Title: Instantaneous response and quantum geometry of insulators

Author: Verma, Nishchhal, Queiroz, Raquel

Issue&Volume: 2025-12-4

Abstract: We present the time-dependent Quantum Geometric Tensor (tQGT) as a comprehensive tool for capturing the geometric character of insulators observable within linear response. We show that tQGT describes the zero-point motion of bound electrons and acts as a generating function for generalized sum rules of electronic conductivity. It therefore enables a systematic framework for computing the instantaneous response of insulators, including optical mass, orbital angular momentum, and dielectric constant. This construction guarantees a consistent approximation across these quantities upon restricting the number of occupied and unoccupied states in a low-energy description of an infinite quantum system. We outline how quantum geometry can be generated in periodic systems by lattice interference and examine spectral weight transfer from small frequencies to high frequencies by creating geometrically frustrated flat bands.

DOI: 10.1073/pnas.2405837122

Source: https://www.pnas.org/doi/abs/10.1073/pnas.2405837122