Title: Introduction to the Quantum Metric
Abstract: In this tutorial talk, I will give an introduction to the concept of quantum metric. Quantum metric assigns “distance” in a parameter space on which quantum states are defined. For example, according to the Bloch theorem, eigenstates of a particle moving in a periodic potential are labeled by a band index and a quasi-momentum. From the Bloch states one can then define the quantum metric, which introduces the measure of distance in (quasi-)momentum space. In recent years, there has been a significant progress in the understanding of physical manifestation/implication of the quantum metric. Effects of the quantum metric are often prominent in flat band systems. Starting from the definition and characterization of the quantum metric, I will review recent theoretical and experimental progress of the study of the quantum metric.