All-to-All interactions via multifractal wavefunction geometry

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.

Figures (2)

• Figure 1: All-to-all interactions and multifractal wavefunctions. (a,d,g) Fibonacci chain with $t_{A}/t_{B}=0.6$ and $N=2585$; (b,e,h) Sierpiǹski gasket of the $7$th generation with magnetic flux $\phi=0.01$; (c,f,i) three-dimensional Anderson model on a $20\times20\times20$ lattice with disorder strength $W=16.5$. The hopping amplitude is set to $t=1$ (with $t_{A}=1$ for the Fibonacci chain). Panels (a-c) show representative single-particle wavefunctions at half filling, where red-highlighted regions labeled $S_i$ denote the $i$th collective spin block. Panels (d-f) display the corresponding multifractal spectra $f(\alpha)$. Panels (g-i) present the zero-temperature effective all-to-all interaction strengths $J_{ij}$ between the spin blocks.
• Figure 2: Time evolution of various entanglement diagnostics following a quench to the effective interaction derived from the Fibonacci chain (green), compared with a short-range Heisenberg model with nearest-neighbor coupling $J_{1}$ and next-nearest-neighbor coupling $J_{2}=J_{1}/5$ (pink), and a Gaussian random interaction with zero mean and standard deviation $0.5$, averaged over 10 disorder realizations (black). (a) Quantum Fisher Information associated with the staggered magnetization operator. (b) Schematic of the subsystem partitioning for the Fibonacci all-to-all system. (c) Tripartite mutual information among subsystems $A$, $B$, and $C$. (d) Bipartite mutual information between subsystem $A$ and subsystem $BC$.