All-to-All Interactions from the Intrinsic Geometry of Multifractal Wavefunctions

We uncover a generic route to all to all interactions arising from the intrinsic geometry of multifractal quantum wavefunctions. By analyzing the multifractal spectrum, a continuous set of scaling exponents, and quantifying the large cross-overlaps between multifractal states, we show how the simultaneous participation of many length scales produces effective global connectivity without external engineering. This mechanism provides a principled pathway to non-local behavior in strongly correlated systems and a framework for realizing long-range many-body phenomena from single-particle criticality.