Title: Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations Show Chinese title

Title: 使用费米黄金规则和克雷默斯-克龙尼格关系将霍尔电导率与多体陈数联系起来

Abstract: This pedagogical piece provides a surprisingly simple demonstration that the quantized Hall conductivity of correlated insulators is given by the many-body Chern number, a topological invariant defined in the space of twisted boundary conditions. In contrast to conventional proofs, generally based on the Kubo formula, our approach entirely relies on combining Kramers-Kronig relations and Fermi's golden rule within a circular-dichroism framework. This pedagogical derivation illustrates how the Hall conductivity of correlated insulators can be determined by monitoring single-particle excitations upon a circular drive, a conceptually simple picture with direct implications for quantum-engineered systems, where excitation rates can be directly monitored. Show Chinese abstract

Abstract: 这个教学性文章提供了一个令人惊讶的简单演示，说明关联绝缘体的量子化霍尔电导率由多体陈数给出，这是一个在扭曲边界条件空间中定义的拓扑不变量。 与通常基于库博公式的传统证明不同，我们的方法完全依赖于在圆偏振框架内结合克朗尼格-凯利关系和费米黄金规则。 这个教学性推导说明了如何通过监测在圆偏振驱动下的单粒子激发来确定关联绝缘体的霍尔电导率，这是一种概念上简单的图像，对量子工程系统有直接的意义，因为在这些系统中激发速率可以直接监测。