On Many-Body Localization for Quantum Spin Chains

Abstract

For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.

62 pages, 4 figures, additional details in section 4 and references for published version. To appear in Jour. Stat. Phys

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• Thermal avalanches in isolated many-body localized systems
• Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
• Signatures of many-body localization and metastability by weak perturbation
• Dynamical Evolution of Entanglement in Disordered Oscillator Systems
• Many-body localization in the droplet spectrum of the random XXZ quantum spin chain
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Localization and slow-thermalization in a cluster spin model
• Lie-Schwinger block-diagonalization and gapped quantum chains: analyticity of the ground-state energy
• Information scrambling and entanglement dynamics in Floquet Time Crystals
• Increasing extractable work in small qubit landscapes
• Statistics of noninteracting many-body fermionic states: The question of a many-body mobility edge
• Quasiconservation Laws and Suppressed Transport in Weakly Interacting Localized Models
• Localization Transition for Interacting Quantum Particles in Colored-Noise Disorder
• Anomalies of global symmetries on the lattice
• Krylov-space anatomy and spread complexity of a disordered quantum spin chain
• Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization
• Numerical and quantum simulation of a quantum disentangled liquid
• Sampling and the complexity of nature
• Lie-Schwinger block-diagonalization and gapped quantum chains
• Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder
• Fluctuation driven transitions in localized insulators: Intermittent metallicity and path chaos precede delocalization
• Long-time properties of generic Floquet systems are approximately periodic with the driving period
• Eigensystem multiscale analysis for Anderson localization in energy intervals
• Asymptotic Localization in the Bose-Hubbard Model
• The robustness condition for general disordered discrete time crystals, and subspace-thermal DTCs from phase transitions between different n-tuple DTCs
• Theoretical study on thermalization in isolated quantum systems
• Fock-space geometry and strong correlations in many-body localized systems
• Quantum Heaviside Eigen Solver
• Scaling Theory of Few-Particle Delocalization
• Reply to Comment on "Discrete Time Crystals: Rigidity Criticality and Realizations"
• Disorder-free localization transition in a two-dimensional lattice gauge theory
• Localization dynamics in a centrally coupled system
• Observation of Localization Using a Noisy Quantum Computer
• Peratic Phase Transition by Bulk-to-Surface Response
• Robustness and Independence of the Eigenstates with respect to the Boundary Conditions across a Delocalization-Localization Phase Transition
• AC Conductivity Crossover in Localized Superconductors
• Scrambling dynamics across a thermalization-localization quantum phase transition
• Many-body localization in a slowly varying potential
• Local density of states and scattering rates across the many-body localization transition
• Krylov complexity of many-body localization: Operator localization in Krylov basis
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
• Many-body localization in large-N conformal mechanics
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain
• Operator delocalization in disordered spin chains via exact MPO marginals
• Beyond the imbalance: site-resolved dynamics probing resonances in many-body localization
• Two-dimensional many-body localized systems coupled to a heat bath
• Information Bounds on phase transitions in disordered systems
• Realizable time crystal of four silicon quantum dot qubits