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Ergodic quantum systems are often quite alike, whereas nonergodic, fractalsystems are unique and display characteristic properties. We explore one ofthese fractal systems, weakly bound dysprosium lanthanide molecules, in anexternal magnetic field. As recently shown, colliding ultracold magneticdysprosium atoms display a soft chaotic behavior with a small degree ofdisorder. We broaden this classification by investigating the generalizedinverse participation ratio and fractal dimensions for large sets of molecularwave functions. Our exact close-coupling simulations reveal a dynamic phasetransition from partially localized states to totally delocalized states anduniversality in its distribution by increasing the magnetic field strength toonly a hundred Gauss (or 10 mT). Finally, we prove the existence of nonergodicdelocalized phase in the system and explain the violation of ergodicity bystrong coupling between near-threshold molecular states and the nearbycontinuum.

Fractal Universality in Near-Threshold Magnetic Lanthanide Dimers