SciPost Physics Core

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.

• Wang et al., Statistics of phase space localization measures and quantum chaos in the kicked top model
  Phys. Rev. E 107, 054213 (2023) [Crossref]
• Monthus, Construction of many-body-localized models where all the eigenstates are matrix-product-states
  J. Stat. Mech. 2020, 083301 (2020) [Crossref]
• Pietracaprina et al., Hilbert-space fragmentation, multifractality, and many-body localization
  Annals of Physics 435, 168502 168502 (2021) [Crossref]
• Sierant et al., Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
  Quantum 6, 638 638 (2022) [Crossref]
• Tang et al., Non-ergodic delocalized phase with Poisson level statistics
  Quantum 6, 733 733 (2022) [Crossref]
• Čadež et al., Machine learning wave functions to identify fractal phases
  Phys. Rev. B 108, 184202 (2023) [Crossref]
• Motamarri et al., Localization and fractality in disordered Russian Doll model
  SciPost Phys. 13, 117 (2022) [Crossref]
• Sierant et al., Universality in Anderson localization on random graphs with varying connectivity
  SciPost Phys. 15, 045 (2023) [Crossref]
• Sierant et al., Universal Behavior beyond Multifractality of Wave Functions at Measurement-Induced Phase Transitions
  Phys. Rev. Lett. 128, 130605 (2022) [Crossref]
• Vallejo-Fabila et al., Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
  Phys. Rev. B 110, 075138 (2024) [Crossref]
• Sarkar et al., Multifractal dimensions for orthogonal-to-unitary crossover ensemble
  34, 033121 (2024) [Crossref]
• Turkeshi et al., Measuring nonstabilizerness via multifractal flatness
  Phys. Rev. A 108, 042408 (2023) [Crossref]
• Orito et al., Multifractality and Fock-space localization in many-body localized states: One-particle density matrix perspective
  Phys. Rev. B 103, 214206 (2021) [Crossref]
• Yoo et al., Open-system spin transport and operator weight dissipation in spin chains
  Phys. Rev. B 107, 115118 (2023) [Crossref]
• Luitz et al., Absence of slow particle transport in the many-body localized phase
  Phys. Rev. B 102, 100202 (2020) [Crossref]
• Taylor et al., Subdiffusion in a one-dimensional Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization
  Phys. Rev. B 103, 184202 (2021) [Crossref]
• Šuntajs et al., Similarity between a many-body quantum avalanche model and the ultrametric random matrix model
  Phys. Rev. Research 6, 023030 (2024) [Crossref]
• Bhakuni et al., Dynamic scaling relation in quantum many-body systems
  Phys. Rev. B 110, 014203 (2024) [Crossref]
• Tarzia, Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
  Phys. Rev. B 105, 174201 (2022) [Crossref]
• Giudici et al., Breakdown of ergodicity in disordered U(1) lattice gauge theories
  Phys. Rev. Research 2, 032034 (2020) [Crossref]
• Solórzano et al., Multifractality and self-averaging at the many-body localization transition
  Phys. Rev. Research 3, L032030 (2021) [Crossref]
• Khaymovich et al., Dynamical phases in a ``multifractal'' Rosenzweig-Porter model
  SciPost Phys. 11, 045 (2021) [Crossref]
• De Tomasi et al., Rare thermal bubbles at the many-body localization transition from the Fock space point of view
  Phys. Rev. B 104, 024202 (2021) [Crossref]
• Kutlin et al., Emergent fractal phase in energy stratified random models
  SciPost Phys. 11, 101 (2021) [Crossref]
• Buijsman et al., Circular Rosenzweig-Porter random matrix ensemble
  SciPost Phys. 12, 082 (2022) [Crossref]
• Fraxanet et al., Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
  Phys. Rev. B 106, 024204 (2022) [Crossref]
• Nakerst et al., Eigenstate thermalization scaling in approaching the classical limit
  Phys. Rev. E 103, 042109 (2021) [Crossref]
• Sarkar et al., Signatures of multifractality in a periodically driven interacting Aubry-André model
  Phys. Rev. B 105, 024301 (2022) [Crossref]
• Łydżba et al., Normal weak eigenstate thermalization
  Phys. Rev. B 110, 104202 (2024) [Crossref]
• Wang et al., Eigenstate Thermalization Hypothesis and Its Deviations from Random-Matrix Theory beyond the Thermalization Time
  Phys. Rev. Lett. 128, 180601 (2022) [Crossref]
• Das et al., Robust nonergodicity of the ground states in the β ensemble
  Phys. Rev. B 109, 064206 (2024) [Crossref]
• Prasad et al., Many-body localization and enhanced nonergodic subdiffusive regime in the presence of random long-range interactions
  Phys. Rev. B 103, 064203 (2021) [Crossref]
• Braemer et al., Pair localization in dipolar systems with tunable positional disorder
  Phys. Rev. B 106, 134212 (2022) [Crossref]
• Tarzia, Many-body localization transition in Hilbert space
  Phys. Rev. B 102, 014208 (2020) [Crossref]
• Nandy et al., Dephasing in strongly disordered interacting quantum wires
  Phys. Rev. B 103, 085105 (2021) [Crossref]
• Das et al., Absence of Mobility Edge in Short-Range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
  Phys. Rev. Lett. 131, 166401 (2023) [Crossref]
• Nandy et al., Delayed thermalization in the mass-deformed Sachdev-Ye-Kitaev model
  Phys. Rev. B 106, 245147 (2022) [Crossref]
• Prasad et al., Initial state dependent dynamics across the many-body localization transition
  Phys. Rev. B 105, 214202 (2022) [Crossref]
• Mattiotti et al., Multifractality in the interacting disordered Tavis-Cummings model
  Phys. Rev. B 109, 064202 (2024) [Crossref]
• Pausch et al., Optimal route to quantum chaos in the Bose–Hubbard model
  J. Phys. A: Math. Theor. 55, 324002 (2022) [Crossref]
• Jana et al., Local density of states and scattering rates across the many-body localization transition
  Phys. Rev. B 104, L140201 (2021) [Crossref]
• Colmenarez et al., Subdiffusive Thouless time scaling in the Anderson model on random regular graphs
  Phys. Rev. B 105, 174207 (2022) [Crossref]
• Deng et al., Anisotropy-mediated reentrant localization
  SciPost Phys. 13, 116 (2022) [Crossref]
• Wang, Quantum Chaos in the Extended Dicke Model
  Entropy 24, 1415 (2022) [Crossref]
• Altshuler et al., Random Cantor sets and mini-bands in local spectrum of quantum systems
  Annals of Physics 456, 169300 169300 (2023) [Crossref]
• Buijsman, Long-range spectral statistics of the Rosenzweig-Porter model
  Phys. Rev. B 109, 024205 (2024) [Crossref]
• Pausch et al., Chaos and Ergodicity across the Energy Spectrum of Interacting Bosons
  Phys. Rev. Lett. 126, 150601 (2021) [Crossref]
• Khaymovich et al., Fragile extended phases in the log-normal Rosenzweig-Porter model
  Phys. Rev. Research 2, 043346 (2020) [Crossref]
• Venturelli et al., Replica approach to the generalized Rosenzweig-Porter model
  SciPost Phys. 14, 110 (2023) [Crossref]
• Sierant et al., Measurement-induced phase transitions in (d+1) -dimensional stabilizer circuits
  Phys. Rev. B 106, 214316 (2022) [Crossref]
• L. Corps et al., Signatures of a critical point in the many-body localization transition
  SciPost Phys. 10, 107 (2021) [Crossref]
• Haque et al., Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
  Phys. Rev. E 105, 014109 (2022) [Crossref]
• Pausch et al., Chaos in the Bose–Hubbard model and random two-body Hamiltonians
  New J. Phys. 23, 123036 (2021) [Crossref]
• Nakerst et al., Chaos in the three-site Bose-Hubbard model: Classical versus quantum
  Phys. Rev. E 107, 024210 (2023) [Crossref]