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We expose two scenarios for the breakdown of quantum multifractality underthe effect of perturbations. In the first scenario, multifractality survivesbelow a certain scale of the quantum fluctuations. In the other one, thefluctuations of the wave functions are changed at every scale and eachmultifractal dimension smoothly goes to the ergodic value. We use as genericexamples a one-dimensional dynamical system and the three-dimensional Andersonmodel at the metal-insulator transition. Based on our results, we conjecturethat the sensitivity of quantum multifractality to perturbation is universal inthe sense that it follows one of these two scenarios depending on theperturbation. We also discuss the experimental implications.

Two scenarios for quantum multifractality breakdown