Speaker
Description
Quantum geometry provides a unifying framework to describe wave-function structure. In this talk, I introduce the quantum metric as a natural tool to characterize non-crystalline quantum matter, as it captures both impurity correlations and localization.
In graphene with vacancy disorder, where defect states form a zero-energy impurity band with multifractal character, a spatially resolved quantum metric reveals strongly enhanced correlations arising from long-range coupling between vacancies. In Fibonacci quasicrystals, the quantum metric likewise characterizes localization by incorporating distances between local symmetry centers. At the same time, the full quantum geometry directly links the localization properties to the fractal energy spectrum.