2019/09/30 by David J. Luitz, Ivan M. Khaymovich, Ivan Khaymovich +1 · 63 citations
Physics and Astronomy · #Anderson localization #Anomalous diffusion #Delocalized electron #Eigenvalues and eigenvectors #Ergodicity #Multifractal system #Physics of Superconductivity and Magnetism #Quantum many-body systems #Series (stratigraphy) #Spins #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.21468/scipostphyscore.2.2.006
published in SciPost Physics Core 2(2) (SciPost.org) · 13 pages, 8 figures
openalex created_date 2019/09/19 · arxiv created 2020/04/01 · openalex publication_date 2020/04/30 · arxiv updated 2020/05/22 · openalex updated_date 2026/08/06
The disordered XXZ model is a prototype model of the many-body localization (MBL) transition. Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due to 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.