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

TL;DR

This paper reviews the role of quantum geometry in correlated electron phases across both flat-band and dispersive-band systems, highlighting its fundamental importance beyond flat-band models.

Contribution

It offers a comprehensive perspective on how quantum geometry influences correlated phases in various band structures, expanding understanding beyond flat-band systems.

Findings

Quantum geometry is crucial in flat-band and dispersive-band correlated phases.

Quantum effects are significant even in dispersive-band systems.

The paper clarifies the role of quantum geometry in diverse electronic phases.

Abstract

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.