Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization

BILEN, A. M.; GEORGEOT, B.; GIRAUD, O.; LEMARIÉ, G.; GARCÍA-MATA, I.

Physical Review Research

American Physical Society

Año: 2021 vol. 3

Quantum multifractality is a fundamental property of systems such as noninteracting disordered systems atan Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence orabsence of a fundamental symmetry related to this property. The anomalous multifractal dimensionqis usedto characterize the structure of quantum states in such systems. Although the multifractal symmetry relation ∆q=∆1−q is universally fulfilled in many known systems, recently some important examples have emergedwhere it does not hold. We show that this is the result of two different mechanisms. The first one was alreadyknown and is related to Gaussian fluctuations well described by random matrix theory. The second one, notpreviously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussianfluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustratethe violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquetcritical system and a model corresponding to Anderson localization on random graphs.