All-to-All interactions via multifractal wavefunction geometry

TL;DR

This paper shows that the complex geometry of multifractal quantum wavefunctions naturally creates effective all-to-all interactions, leading to rapid information scrambling and strong chaos in many-body quantum systems.

Contribution

It introduces a new mechanism where multifractal wavefunction geometry induces global connectivity, bypassing local interaction constraints in many-body systems.

Findings

Multifractal spectrum analysis reveals global connectivity.

Rapid information scrambling evidenced by quantum Fisher information.

Systems with multifractal states are promising for strong chaos regimes.

Abstract

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.