All-to-All interactions via multifractal wavefunction geometry

We uncover a generic mechanism through which the intrinsic geometry of multifractal quantum wavefunctions generates effective all-to-all interactions in many-body systems. By analyzing the multifractal spectrum, we demonstrate that the simultaneous participation of widely separated length scales creates a global connectivity that bypasses local interaction constraints. This nonlocality leads to fast information scrambling, evidenced by sharp changes in the quenched dynamics of the quantum Fisher information and bipartite mutual information with the onset of negative tripartite mutual information. Such rapid scrambling is a defining feature of strongly chaotic quantum dynamics, and our results identify the systems with multifractal states as a promising solid-state platform for realizing this regime. More broadly, they reveal a new paradigm in which complex, multiscale wavefunction structure intrinsically generates long-range connectivity, providing a natural route to achieving nonlocal behavior in strongly correlated quantum materials.