Polynomially filtered exact diagonalization approach to many-body localization

Abstract

Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is introduced. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target by a spectral transformation using a high order polynomial of the matrix. The memory requirements scale better with system size than in the state-of-the-art shift-invert approach. The potential of POLFED is demonstrated examining many-body localization transition in 1D interacting quantum spin-1/2 chains. We investigate the disorder strength and system size scaling of Thouless time. System size dependence of bipartite entanglement entropy and of the gap ratio highlights the importance of finite-size effects in the system. We discuss possible scenarios regarding the many-body localization transition obtaining estimates for the critical disorder strength.

4+5 pages, version accepted in Physical Review Letters, comments welcome

References in corpus (23)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• A Density Matrix-based Algorithm for Solving Eigenvalue Problems
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Many-body localization dynamics from gauge invariance
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Can we study the many-body localisation transition?
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Many-body localization due to random interactions
• Many body localization with long range interactions
• Many-body localization in infinite chains
• Renormalization-group study of the many-body localization transition in one dimension
• Absence of full many-body localization in the disordered Hubbard chain
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• Many-Body Localization in System with a Completely Delocalized Single-Particle Spectrum
• Coexistence of localized and extended phases: Many-body localization in a harmonic trap
• Many-body localization in Ising models with random long-range interactions

Cited by in corpus (112)

• Avalanches and many-body resonances in many-body localized systems
• Challenges to observation of many-body localization
• Absence of true localization in many-body localized phases
• Markovian baths and quantum avalanches
• Many-Body Localization in the Age of Classical Computing
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Probing many-body quantum chaos with quantum simulators
• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
• Thermalization of dilute impurities in one dimensional spin chains
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Eigenstate correlations around many-body localization transition
• Many-body localization in a fragmented Hilbert space
• Many-body localization of bosons in optical lattice: Dynamics in disorder-free potentials
• Stability of many-body localization in Floquet systems
• Resonance-induced growth of number entropy in strongly disordered systems
• Finite-Size scaling analysis of many-body localization transition in quasi-periodic spin chains
• Optimised Trotter Decompositions for Classical and Quantum Computing
• Universality in Anderson localization on random graphs with varying connectivity
• Many-body localization in tilted and harmonic potentials
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Many-body quantum chaos in stroboscopically-driven cold atoms
• Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition
• Constraints induced delocalization
• Multifractality and self-averaging at the many-body localization transition
• Many-body localization in large systems: Matrix-product-state approach
• Scaling of Fock-space propagator and multifractality across the many-body localization transition
• The internal clock of many-body delocalization
• Detecting delocalization-localization transitions from full density distributions
• Delayed Thermalization in Mass-Deformed SYK
• Nonergodic dynamics in disorder-free potentials
• Scale-Invariant Survival Probability at Eigenstate Transitions
• Interaction-Driven Instabilities in the Random-Field XXZ Chain
• Mobility edge in long-range interacting many-body localized systems
• Localization challenges quantum chaos in the finite two-dimensional Anderson model
• Role of Fock-space correlations in many-body localization
• Catching thermal avalanches in the disordered XXZ model
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Detecting ergodic bubbles at the crossover to many-body localization using neural networks
• Recent progress on quantum simulations of non-standard Bose-Hubbard models
• Many-body delocalization from embedded thermal inclusion
• Dephasing in strongly disordered interacting quantum wires
• Restoring ergodicity in a strongly disordered interacting chain
• Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems
• Polynomial filter diagonalization of large Floquet unitary operators
• Colloquium: Synthetic quantum matter in non-standard geometries
• Many-Body Mobility Edge in Quantum Sun models
• The Fock-space landscape of many-body localisation
• Ergodicity breaking with long range cavity induced quasiperiodic interactions
• Loschmidt echo singularities as dynamical signatures of strongly localized phases
• Stable many-body localization under random continuous measurements in the no-click limit
• Slow dynamics of a mobile impurity interacting with an Anderson insulator
• Information-Theoretic Memory Scaling in the Many-Body Localization Transition
• Nonstabilizerness dynamics in many-body localized systems
• Slow diffusion and Thouless localization criterion in modulated spin chains
• Destruction of Localization by Thermal Inclusions: Anomalous Transport and Griffiths Effects in the Anderson and André-Aubry-Harper Models
• Ergodic inclusions in many body localized systems
• Many-Body Localization: Transitions in Spin Models
• Absence of localization in two-dimensional Clifford circuits
• An analysis of localization transitions using non-parametric unsupervised learning
• Statistics of systemwide correlations in the random-field XXZ chain: Importance of rare events in the many-body localized phase
• Pair localization in dipolar systems with tunable positional disorder
• Fermionic Magic Resources of Quantum Many-Body Systems
• Many body localization transition with correlated disorder
• The Coming Decades of Quantum Simulation
• Thermalization propagation front and robustness against avalanches in localized systems
• Strongly disordered Anderson insulator chains with generic two-body interaction
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Phenomenology of many-body localization in bond-disordered spin chains
• Finite-size prethermalization at the chaos-to-integrable crossover
• Cat states carrying long-range correlations in the many-body localized phase
• Many-body localization regime for cavity induced long-range interacting models
• Computing quantum magic of state vectors
• Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions
• Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition
• Many-body localization and delocalization dynamics in the thermodynamic limit
• Many-body localized to ergodic transitions in a system with correlated disorder
• Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain
• The role of interaction-induced tunneling in the dynamics of polar lattice bosons
• Finite steady-state current defies non-Hermitian many-body localization
• Tracking locality in time evolution of disordered systems
• Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Non-Hermitian Multipole Skin Effects Challenge Localization
• Interacting quasiperiodic spin chains in the prethermal regime
• From Dyson Models to Many-Body Quantum Chaos
• Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
• Inhomogeneous Floquet thermalization
• Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition
• DanceQ: High-performance library for number-conserving bases
• Scaling theory of fading ergodicity
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Nonergodic dynamics for an impurity interacting with bosons in tilted lattice
• 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
• Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
• Random cubic graph embedded in a hypercube: Entanglement spectrum and many-body localization
• Numerical methods for localization
• Memory efficient Fock-space recursion scheme for computing many-fermion resolvents
• Orthogonal layers of parallelism in large-scale eigenvalue computations
• Long-range resonances in quasiperiodic many-body localization
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath
• Anomalous transport in U(1)-symmetric quantum circuits
• Anderson Localization on Husimi Trees and its implications for Many-Body localization
• Beyond the imbalance: site-resolved dynamics probing resonances in many-body localization
• A link between static and dynamical perturbation theory
• Universal Relation between Spectral and Wavefunction Properties at Criticality
• Inner structure of the many-body localization transition and the fulfillment of the Harris criterion
• Many-body localization and particle multioccupancy in the disordered Bose-Hubbard model
• Unsupervised Techniques to Detect Quantum Chaos
• Statistics-encoded tensor network approach in disordered quantum many-body spin chains
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain