Clarify quantum geometry in strongly correlated systems

Determine how the quantum geometric tensor and related geometric quantities (such as the quantum metric and Berry curvature) manifest in strongly correlated phases, including Mott insulators, quantum spin liquids, and unconventional superconductors, and establish experimental and theoretical frameworks that can reliably characterize these manifestations beyond single-particle band descriptions.

Background

Most current experimental studies of quantum geometry focus on weakly interacting materials where single-particle band structures provide a good approximation. Extending these concepts to strongly correlated systems is nontrivial because electron-electron interactions can qualitatively alter quasiparticles, excitations, and emergent gauge structures.

Resolving how the quantum geometric tensor and its components (quantum metric and Berry curvature) appear in correlated phases would bridge band-geometry formalisms with many-body physics, enabling geometric interpretations of phenomena such as Mott transitions, spin-liquid excitations, and unconventional pairing mechanisms.