Emergence of non-ergodic multifractal quantum states in geometrical fractals

TL;DR

This paper introduces a method to create non-ergodic multifractal quantum states in crystalline structures by fractalizing the lattice, revealing new quantum transport phenomena without relying on disorder.

Contribution

It demonstrates a novel way to generate non-ergodic multifractal states through fractal lattice design, expanding the understanding of quantum states beyond disorder-based models.

Findings

Evidence of non-ergodic multifractal states in fractal lattices

Robust quantum states beyond conventional classifications

Potential experimental signatures discussed

Abstract

Eigenstate multifractality, a hallmark of non-interacting disordered metals, which may also be observed in many-body localized states, is characterized by anomalous slow dynamics and appears relevant for many areas of quantum physics, from measurement-driven systems to superconductivity. We propose a novel approach to achieve non-ergodic multifractal states (NEMs) without disorder by iteratively introducing defects into a crystal lattice, reshaping it from a plain structure into a fractal geometry. By comprehensive analysis of the Sierpi\'nski gasket case, we find robust evidence of the emergence of NEMs that go beyond the conventional classification of quantum states and designate new pathways for quantum transport studies. We discuss potential experimental signatures of these states.