TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.1.008
TI  - Anatomy of the eigenstates distribution: A quest for a genuine multifractality
PY  - 2024/01/09
UR  - https://scipost.org/SciPostPhys.16.1.008
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 1
SP  - 008
A1  - Kutlin, Anton
AU  - Khaymovich, Ivan M.
AB  - Motivated by a series of recent works, an interest in multifractal phases has risen as they are believed to be present in the Many-Body Localized (MBL) phase and are of high demand in quantum annealing and machine learning. Inspired by the success of the Rosenzweig-Porter (RP) model with Gaussian-distributed hopping elements, several RP-like ensembles with the fat-tailed distributed hopping terms have been proposed, with claims that they host the desired multifractal phase. In the present work, we develop a general (graphical) approach allowing a self-consistent analytical calculation of fractal dimensions for a generic RP model and investigate what features of the RP Hamiltonians can be responsible for the multifractal phase emergence. We conclude that the only feature contributing to a genuine multifractality is the on-site energies' distribution, meaning that no random matrix model with a statistically homogeneous distribution of diagonal disorder and uncorrelated off-diagonal terms can host a multifractal phase.
ER  -

@Article{10.21468/SciPostPhys.16.1.008,
	title={{Anatomy of the eigenstates distribution: A quest for a genuine multifractality}},
	author={Anton Kutlin and Ivan M. Khaymovich},
	journal={SciPost Phys.},
	volume={16},
	pages={008},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.1.008},
	url={https://scipost.org/10.21468/SciPostPhys.16.1.008},
}