# Fractal Universality in Near-Threshold Magnetic Lanthanide Dimers

## TL;DR

This paper investigates the fractal and nonergodic properties of dysprosium lanthanide molecules in magnetic fields, revealing a phase transition and universality in their quantum states, with implications for understanding complex quantum systems.

## Contribution

It introduces a detailed analysis of fractal dimensions and phase transitions in near-threshold molecular states, demonstrating universality and nonergodic delocalized phases in these systems.

## Key findings

- Identification of a dynamic phase transition from localized to delocalized states.
- Evidence of universality in the distribution of fractal dimensions with increasing magnetic field.
- Existence of a nonergodic delocalized phase caused by strong coupling to the continuum.

## Abstract

Ergodic quantum systems are often quite alike, whereas nonergodic, fractal systems are unique and display characteristic properties. We explore one of these fractal systems, weakly bound dysprosium lanthanide molecules, in an external magnetic field. As recently shown, colliding ultracold magnetic dysprosium atoms display a soft chaotic behavior with a small degree of disorder. We broaden this classification by investigating the generalized inverse participation ratio and fractal dimensions for large sets of molecular wave functions. Our exact close-coupling simulations reveal a dynamic phase transition from partially localized states to totally delocalized states and universality in its distribution by increasing the magnetic field strength to only a hundred Gauss (or 10 mT). Finally, we prove the existence of nonergodic delocalized phase in the system and explain the violation of ergodicity by strong coupling between near-threshold molecular states and the nearby continuum.

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Source: https://tomesphere.com/paper/1802.09586