Symmetry violation of quantum multifractality: Gaussian fluctuations versus algebraic localization
Abstract
Quantum multifractality is a fundamental property of systems such as noninteracting disordered systems at an Anderson transition and manybody systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension Δ_{q} is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation Δ_{q}=Δ_{1 −q} is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that this is the result of two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.
 Publication:

Physical Review Research
 Pub Date:
 June 2021
 DOI:
 10.1103/PhysRevResearch.3.L022023
 arXiv:
 arXiv:2103.03068
 Bibcode:
 2021PhRvR...3b2023B
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Quantum Physics
 EPrint:
 Closest to published version