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 3
G. Giudici et al., Breakdown of ergodicity in disordered
lattice gauge theories
Phys. Rev. Research 2, 032034 (2020) [Crossref]
CÃ©cile Monthus, Construction of many-body-localized models where all the eigenstates are matrix-product-states
J. Stat. Mech. 2020, 083301 (2020) [Crossref]
M. Tarzia, Many-body localization transition in Hilbert space
Phys. Rev. B 102, 014208 (2020) [Crossref]
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- 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]