Quantum geometry in correlated electron phases: from flat band to dispersive band

Quantum geometry, describing the geometric properties of the Bloch wave function in momentum space, has recently been recognized as a fundamental concept in condensed matter physics. The flat-band system offers the paradigmatic platform where quantum geometry plays the essential role in correlated electron phases. However, systems that suffer from significant effects of quantum geometry are not limited to flat-band systems; dispersive-band systems also exhibit quantum condensed phases driven by quantum geometry. In this perspective, we provide a transparent account of quantum geometry and its role in correlated electron phases, throughout flat-band and dispersive-band systems.