Abstract

Fractals, with their self-similar and scale-invariant structures, have long fascinated researchers across many disciplines. Beyond their aesthetic and geometric appeal, fractal geometry profoundly impacts quantum systems, determining wavefunction properties, transport phenomena, and localization behavior in ways that challenge conventional knowledge.
In this talk, we will first explore the fundamental properties of geometrical fractals and their emerging role in quantum physics. By linking these features to eigenstate multifractality—a hallmark of disordered metals and a key factor in many-body localization, leading to anomalously slow dynamics—we introduce a novel approach to realizing non-ergodic multifractal (NEM) states without random disorder. This can be achieved by modifying a crystal lattice into a fractal geometry through iterative defect placement.
Through a comprehensive analysis of the Sierpiński gasket as a model system, we will provide robust evidence for the emergence of NEM states that go beyond the standard classifications of quantum states. Furthermore, potential experimental signatures will also be discussed, particularly through the study of the two-points correlator function and the quantum dynamics of a single particle.

Ref: arXiv:2410.18559