Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
David J. Luitz, Ivan M. Khaymovich, Yevgeny Bar Lev
SciPost Phys. Core 2, 006 (2020) · published 30 April 2020
- doi: 10.21468/SciPostPhysCore.2.2.006
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Abstract
The disordered XXZ model is a prototype model of the many-body localization transition (MBL). Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.
Cited by 56
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Max-Planck-Institut für Physik komplexer Systeme / Max Planck Institute for the Physics of Complex Systems
- 2 אוניברסיטת בן-גוריון בנגב / Ben-Gurion University of the Negev [BGU]
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- Israel Science Foundation [ISF]
- Partnership for Advanced Computing in Europe AISBL (PRACE) (through Organization: Partnership for Advanced Computing in Europe [PRACE])
- Российский фонд фундаментальных исследований / Russian Foundation for Basic Research [RFBR]