标题： 量子材料中的量子几何 显示英文标题

标题： Quantum Geometry in Quantum Materials

摘要： 量子几何由量子几何张量表征，在量子材料中的各种物理现象中起着关键作用。 在凝聚态系统中，量子几何指的是布里渊区中布洛赫态的几何性质。 这篇教学性综述提供了对量子几何概念的易于理解的介绍，并强调了其在多个领域中的广泛影响。 具体而言，我们讨论了量子几何在光学响应、朗道能级和分数陈绝缘体中的作用，以及其对超流体重量、自旋刚度、激子凝聚体、电子-声子耦合等的影响。 通过整合这些主题，我们强调了量子几何在理解量子材料中出现的行为中的普遍重要性。 最后，我们提出了开放性问题和潜在的未来方向，突出了在这个迅速发展的领域中持续探索的必要性。 显示英文摘要

摘要： Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the Brillouin zone. This pedagogical review provides an accessible introduction to the concept of quantum geometry, emphasizing its extensive implications across multiple domains. Specifically, we discuss the role of quantum geometry in optical responses, Landau levels, and fractional Chern insulators, as well as its influence on superfluid weight, spin stiffness, exciton condensates, electron-phonon coupling, etc. By integrating these topics, we underscore the pervasive significance of quantum geometry in understanding emergent behaviors in quantum materials. Finally, we present an outlook on open questions and potential future directions, highlighting the need for continued exploration in this rapidly developing field.