Multifractal Scalings across the Many-Body Localization Transition

Abstract

In contrast with Anderson localization where a genuine localization is observed in real space, the many-body localization (MBL) problem is much less understood in the Hilbert space, support of the eigenstates. In this work, using exact diagonalization techniques we address the ergodicity properties in the underlying $\mathcal{N}$-dimensional complex networks spanned by various computational bases for up to $L=24$ spin-1/2 particles (i.e. Hilbert space of size $\mathcal{N}\simeq 2.710^6$). We report fully ergodic eigenstates in the delocalized phase (irrespective of the computational basis), while the MBL regime features a generically (basis-dependent) multifractal behavior, delocalized but non-ergodic. The MBL transition is signaled by a non-universal jump of the multifractal dimensions.

arXiv commentFinal version accepted in Phys. Rev. Lett. (including supplemental material)

References in corpus (64)

• Chaos and Quantum Thermalization
• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Many-body localization, thermalization, and entanglement
• The many-body localization phase transition
• Many-body localization edge in the random-field Heisenberg chain
• Unbounded growth of entanglement in models of many-body localization
• Many body localization in Heisenberg XXZ magnet in a random field
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Many-body localization: an introduction and selected topics
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Universal slow growth of entanglement in interacting strongly disordered systems
• Area laws in a many-body localized state and its implications for topological order
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Recent progress in many-body localization
• Absence of diffusion in an interacting system of spinless fermions on a one-dimensional disordered lattice
• Extended slow dynamical regime close to the many-body localization transition
• The Ergodic Side of the Many-Body Localization Transition
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• A criterion for many-body localization-delocalization phase transition
• Ergodicity breaking in a model showing many-body localization
• Two universality classes for the many-body localization transition
• Review: Local Integrals of Motion in Many-Body Localized systems
• Rare region effects and dynamics near the many-body localization transition
• Critical Properties of the Many-Body Localization Transition
• Many-body delocalization as a quantum avalanche
• Many-body localization and delocalization in large quantum chains
• Anderson localization on random regular graphs
• Early breakdown of area-law entanglement at many-body delocalization transition
• Thouless energy and multifractality across the many-body localization transition
• Non-ergodic phases in strongly disordered random regular graphs
• Analytically solvable renormalization group for the many-body localization transition
• Scaling theory of the Anderson transition in random graphs: ergodicity and universality
• Many-body localization transition in a lattice model of interacting fermions: statistics of renormalized hoppings in configuration space
• Kosterlitz-Thouless scaling at many-body localization phase transitions
• Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay
• Shift-invert diagonalization of large many-body localizing spin chains
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• Statistics of eigenstates near the localization transition on random regular graphs
• Non-ergodic metallic and insulating phases of Josephson junction chains
• Scaling Theory of Entanglement at the Many-Body Localization Transition
• Extended nonergodic states in disordered many-body quantum systems
• Return probability for the Anderson model on the random regular graph
• Many-body localization transition with power-law interactions: Statistics of eigenstates
• Spin transport of weakly disordered Heisenberg chain at infinite temperature
• Typicality approach to the optical conductivity in thermal and many-body localized phases
• Critical properties of the Anderson localization transition and the high dimensional limit
• Dynamical conductivity and its fluctuations along the crossover to many-body localization
• Multiscale entanglement clusters at the many-body localization phase transition
• Many-body localization and delocalization from the perspective of Integrals of Motion
• Many-body localization in Fock-space: a local perspective
• Multifractal metal in a disordered Josephson Junction Array
• Spectral diffusion and scaling of many-body delocalization transitions
• Percolation in Fock space as a proxy for many-body localisation
• Exact solution of a percolation analogue for the many-body localisation transition
• Reduced-basis approach to many-body localization
• Many-body localization in the Fock space of natural orbitals
• Multifractality of quantum wave functions in the presence of perturbations

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