Many-Body Localization in the Age of Classical Computing
arXiv:2403.07111 · doi:10.1088/1361-6633/ad9756
Abstract
Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. Persistent finite size drifts towards ergodicity consistently emerge in spectral properties of disordered many-body systems, excluding naive single-parameter scaling hypothesis and preventing comprehension of the status of the MBL phase. The drifts are related to tendencies towards thermalization and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength suggests the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations.
75 pages, 14 figures, updated version
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- Many-Body Localization in System with a Completely Delocalized Single-Particle Spectrum
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- Universal dynamics of density correlations at the transition to many-body localized state
- Asymmetry in energy versus spin transport in certain interacting, disordered systems
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- Localisation on certain graphs with strongly correlated disorder
- Many-body localization in presence of cavity mediated long-range interactions
- Energy diffusion in the ergodic phase of a many body localizable spin chain
- Exploring many-body localization in quantum systems coupled to an environment via Wegner-Wilson flows
- Phenomenology of spectral functions in disordered spin chains at infinite temperature
- Strong many-particle localization and quantum computing with perpetually coupled qubits
- Fidelity susceptibility in Gaussian Random Ensembles
- Unlimited growth of particle fluctuations in many-body localized phases
- Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
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- Many-body localization in Ising models with random long-range interactions
- Discrete disorder models for many-body localization
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- Relaxation at different length-scales in models of many-body localization
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- Flow Equations for Disordered Floquet Systems
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- Subdiffusion in one-dimensional Hamiltonian chains with sparse interactions
- Density-Matrix Renormalization Group study of Many-Body Localization in Floquet Eigenstates
- Superposition and higher-order spacing ratios in random matrix theory with application to complex systems
- Chaos and subdiffusion in the infinite-range coupled quantum kicked rotors
- Entropy and Temperature in finite isolated quantum systems
- Slow diffusion and Thouless localization criterion in modulated spin chains
- Charge and spin-specific local integrals of motion in a disordered Hubbard model
- Diffusion in the Anderson model in higher dimensions
- Emergent dipole moment conservation and subdiffusion in tilted chains
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- Spatio-temporal heterogeneity of entanglement in many-body localized systems
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- Quantum chaos and level dynamics
- Strongly disordered Anderson insulator chains with generic two-body interaction
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Cited by in corpus (107)
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- Graph theory and tunable slow dynamics in quantum East Hamiltonians
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- Taking the temperature of quantum many-body scars
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- Multifractality in high-dimensional graphs induced by correlated radial disorder
- Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
- Characterizing the Many Body Localization Crossover as a Metal-Insulator Transition: Localization length from Polarization and Quantum Metric
- Sub-ballistic operator growth in spin chains with heavy-tailed random fields
- Discrete time crystals enhanced by Stark potentials in Rydberg atom arrays
- Thermal avalanches in isolated many-body localized systems
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- Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
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- Krylov-space anatomy and spread complexity of a disordered quantum spin chain
- Anderson localisation in spatially structured random graphs
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- The Wishart--Rosenzweig--Porter random matrix ensemble
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- The ITransverse.jl library for transverse tensor network contractions
- Anomalies of global symmetries on the lattice
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- Characterization of the chaotic phase in the tilted Bose-Hubbard model
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- Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation
- 2D Anderson Localization and KPZ sub-Universality Classes : sensitivity to boundary conditions and insensitivity to symmetry classes
- Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach
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- Statistics-encoded tensor network approach in disordered quantum many-body spin chains
- Imaginary Time Spectral Transforms for Excited State Preparation
- From Bell Products to Greenberger-Horne-Zeilinger states: Quantum Memories via emergent Hamiltonians
- Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
- Fock space prethermalization and time-crystalline order on a quantum processor
- Quantum Complexity in Rule-Based Constrained Many-Body Models: Scars, Fragmentation, and Chaos
- Large deviations in the many-body localization transition: The case of the random-field XXZ chain
- Qudit-native measurement protocol for dynamical correlations using Hadamard tests
- Loop Charges and Fragmentation in Pairwise Difference Conserving Circuits
- Charge carrier relaxation dynamics in the one-dimensional Kondo lattice model
- Coherently synchronized oscillations in many-body localization
- From Bose glass to many-body localization in a one-dimensional disordered Bose gas
- Unified theory of local integrals of motion
- Temperature and conditions for thermalization after canonical quenches
- Anderson Localization on Husimi Trees and its implications for Many-Body localization
- Rationally independent free fermions with local hopping
- Operator delocalization in disordered spin chains via exact MPO marginals
- Crossover from Quantum Chaos to a Reversed Quantum Disentangled Liquid in a Disorder-Free Spin Ladder
- Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry
- Limits of Clifford Disentangling in Tensor Network States
- Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
- Many-body spectral transitions through the lens of the variable-range SYK2 model
- Controlling discrete time crystals via single-site operations in zero-field diamond quantum simulators