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The disordered XXZ model is a prototype model of the many-body localizationtransition (MBL). Despite numerous studies of this model, the availablenumerical evidence of multifractality of its eigenstates is not very conclusivedue severe finite size effects. Moreover it is not clear if similarly to thecase of single-particle physics, multifractal properties of the many-bodyeigenstates are related to anomalous transport, which is observed in thismodel. In this work, using a state-of-the-art, massively parallel, numericallyexact method, we study systems of up to 24 spins and show that a large fractionof the delocalized phase flows towards ergodicity in the thermodynamic limit,while a region immediately preceding the MBL transition appears to bemultifractal in this limit. We discuss the implication of our finding on themechanism of subdiffusive transport.

Multifractality and its role in anomalous transport in the disordered XXZ spin-chain