Hilbert-space correlations beyond multifractality and bipartite entanglement in many-body localised systems
arXiv:2208.08468 · doi:10.1103/PhysRevB.106.L140204
Abstract
Eigenstates of many-body localised (MBL) systems are characterised by area-law bipartite entanglement along with multifractal statistics of their amplitudes on Hilbert space. At the same time, sparse random pure states with fractal statistics are not compatible with area-law and necessarily exhibit volume-law entanglement. This raises the question that what correlation functions of Hilbert-space amplitudes MBL eigenstates must possess for their area law entanglement to be compatible with their multifractality. In this work, we identify and compute such appropriate Hilbert-space correlations which carry information of entanglement. We find that, for MBL eigenstates, these correlations are qualitatively different not only from those of ergodic states but also of sparse random states with fractal statistics. This enables us to show that indeed the said correlations lie at the heart of the coexistence of area-law entanglement and multifractality for MBL eigenstates.
arXiv comment6 pages, 5 figures + supplementary material (2 pages, 1 figure), version published in Phys. Rev. B as a Letter
References in corpus (42)
- Many body localization and thermalization in quantum statistical mechanics
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Localization of interacting fermions at high temperature
- Many-body localization, thermalization, and entanglement
- Average Entropy of a Subsystem
- 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
- 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
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Many-body localization: an introduction and selected topics
- On Many-Body Localization for Quantum Spin Chains
- Universal slow growth of entanglement in interacting strongly disordered systems
- Measurement-driven entanglement transition in hybrid quantum circuits
- Area laws in a many-body localized state and its implications for topological order
- Quantum chaos challenges many-body localization
- Recent progress in many-body localization
- Avalanches and many-body resonances in many-body localized systems
- Multifractal Scalings across the Many-Body Localization Transition
- Ergodicity breaking in a model showing many-body localization
- Review: Local Integrals of Motion in Many-Body Localized systems
- Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
- Critical Properties of the Many-Body Localization Transition
- Distinguishing localization from chaos: challenges in finite-size systems
- Low-frequency conductivity in many-body localized systems
- Many body localization and thermalization: insights from the entanglement spectrum
- Markovian baths and quantum avalanches
- Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
- Rare thermal bubbles at the many-body localization transition from the Fock space point of view
- A constructive theory of the numerically accessible many-body localized to thermal crossover
- Renyi Entropy of Chaotic Eigenstates
- Multifractality meets entanglement: relation for non-ergodic extended states
- Local resonances and parametric level dynamics in the many-body localised phase
- Fock-space anatomy of eigenstates across the many-body localisation transition
- Characterizing the many-body localization transition through the entanglement spectrum
- Phenomenology of spectral functions in disordered spin chains at infinite temperature
- Resonant energy scales and local observables in the many-body localised phase
- Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
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- Probability transport on the Fock space of a disordered quantum spin chain
- The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains
- Entanglement dynamics and eigenstate correlations in strongly disordered quantum many-body systems
- Anatomy of localisation protected quantum order on Hilbert space
- Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
- Krylov-space anatomy and spread complexity of a disordered quantum spin chain