We review recent progresses in the study of flat band systems, especially focusing on the
fundamental physics related to the singularity of the flat band's Bloch wave functions. We first …

Quantum geometry defines the phase and amplitude distances between quantum states.
The phase distance is characterized by the Berry curvature and thus relates to topological …

Topological physics relies on the structure of the eigenstates of the Hamiltonians. The
geometry of the eigenstates is encoded in the quantum geometric tensor—comprising the …

We investigate relations between topology and the quantum metric of two-dimensional
Chern insulators. The quantum metric is the Riemannian metric defined on a parameter …

Topological pumps have garnered substantial attention in physics. However, the
requirement for slow evolution speed to satisfy adiabaticity greatly restricts their application …

Understanding the geometric properties of quantum states and their implications in
fundamental physical phenomena is a core aspect of contemporary physics. The quantum …

A Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is
well studied in many branches of modern physics; however, the quantum metric as a real …

The geometry of Hamiltonian's eigenstates is encoded in the quantum geometric tensor
(QGT), containing both the Berry curvature, central to the description of topological matter …

In Hilbert space, the geometry of the quantum state is identified by the quantum geometric
tensor (QGT), whose imaginary part is the Berry curvature and whose real part is the …

Geometry and topology are fundamental concepts, which underlie a wide range of
fascinating physical phenomena such as topological states of matter and topological …