Berry curvature physics and quantum geometric effects have been instrumental in
advancing topological condensed matter physics in recent decades. Although Landau level …

We show that the static structure factor of general many-body systems with U (1) symmetry
has a lower bound determined only by the ground state Chern number. Our bound relies …

Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse
physical phenomena in quantum materials. In condensed matter systems, quantum …

We establish a universal relation between the energy gap and the static dielectric constant
for all insulating states. This relation yields an upper bound on the energy gap, which only …

Flat bands that do not merely arise from weak interactions can produce exotic physical
properties, such as superconductivity or correlated many-body effects. The quantum metric …

Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a
powerful approach to understanding quantum systems. When the measured region has …

Probing the quantum geometry and topology in condensed matter systems has relied
heavily on static electronic transport experiments in magnetic fields. Yet, contact-free optical …

The spread of valence-band Wannier functions in semiconductors and insulators is a
characteristic property that gives a rough estimation of how insulating is the material. We …

Conductivity in a multiband system can be divided into intra-and interband contributions,
and the latter further into symmetric and antisymmetric parts. In a flat band, intraband …

We introduce the concept of quantum weight as a fundamental property of quantum many-
body systems that is encoded in the ground-state static structure factor and characterizes …