Correlation-induced localization

Abstract

A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A new class of random Hamiltonians with translation-invariant hopping integrals is suggested and the localization properties of such models are established both in the coordinate and in the momentum spaces alongside with the corresponding level statistics. Duality of translation-invariant models in the momentum and coordinate space is uncovered and exploited to find a full localization-delocalization phase diagram for such models. The crucial role of the spectral properties of hopping matrix is established and a new matrix inversion trick is suggested to generate a one-parameter family of equivalent localization/delocalization problems. Optimization over the free parameter in such a transformation together with the localization/delocalization principles allows to establish exact bounds for the localized and ergodic states in long-range hopping models. When applied to the random matrix models with deterministic power-law hopping this transformation allows to confirm localization of states at all values of the exponent in power-law hopping and to prove analytically the symmetry of the exponent in the power-law localized wave functions.

arXiv comment14 pages, 8 figures + 5 pages, 2 figures in appendices

References in corpus (65)

• Anderson Transitions
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Anderson localization of a non-interacting Bose-Einstein condensate
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Observation of entanglement propagation in a quantum many-body system
• Non-local propagation of correlations in long-range interacting quantum systems
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• Many-body Localization with Dipoles
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• A random matrix model with localization and ergodic transitions
• Thermodynamics and dynamics of systems with long-range interactions
• Dynamical phase diagram of spin chains with long-range interactions
• Multifractal finite-size-scaling and universality at the Anderson transition
• New Class of Random Matrix Ensembles with Multifractal Eigenvectors
• Griffiths effects and slow dynamics in nearly many-body localized systems
• Quantum Spin Dynamics with Pairwise-Tunable, Long-Range Interactions
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• Correlations of Nearby Levels Induced by a Random Potential
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• 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
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Return probability for the Anderson model on the random regular graph
• Many body localization with long range interactions
• Many-body localization transition with power-law interactions: Statistics of eigenstates
• Localization in a random $x-y$ model with the long-range interaction: Intermediate case between single particle and many-body problems
• Delocalized Glassy Dynamics and Many Body Localization
• Duality in power-law localization in disordered one-dimensional systems
• Transitions toward Quantum Chaos: with Supersymmetry from Poisson to Gauss
• Self-dual quasiperiodic systems with power-law hopping
• Eigenfunction distribution for the Rosenzweig-Porter model
• Shielding and localization in presence of long range hopping
• Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Dynamical phase transitions in the two-dimensional transverse-field Ising model
• Localization properties of a one-dimensional tight-binding model with non-random long-range inter-site interactions
• Non-Ergodic Delocalization in the Rosenzweig-Porter Model
• Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
• Multifractal metal in a disordered Josephson Junction Array
• Spectral diffusion and scaling of many-body delocalization transitions
• Emergent locality in systems with power-law interactions
• Algebraic Many-Body Localization and its implications on information propagation
• Transition from Poisson to gaussian unitary statistics: The two-point correlation function
• Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime
• Effect of long-range hopping and interactions on entanglement dynamics and many-body localization
• Integrals of motion for one-dimensional Anderson localized systems
• Perturbation Theory for the Rosenzweig-Porter Matrix Model
• Level-statistics in Disordered Systems: A single parametric scaling and Connection to Brownian Ensembles
• Alternative Technique for "Complex" Spectra Analysis
• The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models
• Temperature inversion in long-range interacting systems
• The effect of anisotropy of long-range hopping on localization in three-dimensional lattices
• Spread of wave packets in disordered hierarchical lattices
• Disorder-driven transition in a chain with power-law hopping
• Anderson localization on a simplex
• Phase coherence in tight-binding models with nonrandom long-range hopping
• Surprises from quenches in long-range interacting systems: Temperature inversion and cooling
• Velocity filtration and temperature inversion in a system with long-range interactions
• The Phase Transition in the Ultrametric Ensemble and Local Stability of Dyson Brownian Motion
• Support set of random wave-functions on the Bethe lattice
• Effect of Hilbert space truncation on Anderson localization

Cited by in corpus (79)

• Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
• The Many-Body localization transition in the Hilbert space
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Sub-diffusion in the Anderson model on random regular graph
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Disorder-Enhanced and Disorder-Independent Transport with Long-Range Hopping: Application to Molecular Chains in Optical Cavities
• Fock-space correlations and the origins of many-body localisation
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Multifractality meets entanglement: relation for non-ergodic extended states
• Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble
• Anomalous transport through algebraically localized states in one-dimension
• From ergodic to non-ergodic chaos in Rosenzweig-Porter model
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Emergent fractal phase in energy stratified random models
• On super-Poissonian behavior of the Rosenzweig-Porter model in the non-ergodic extended regime
• Non-ergodic delocalized phase with Poisson level statistics
• Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions
• Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
• Localisation on certain graphs with strongly correlated disorder
• Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder
• Critical-to-Insulator Transitions and Fractality Edges in Perturbed Flatbands
• Flat-band-based multifractality in the all-band-flat diamond chain
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
• Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
• Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
• Out of equilibrium Phase Diagram of the Quantum Random Energy Model
• Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Anisotropy-mediated reentrant localization
• Many-body localization in long range model: Real space renormalization group study
• Renormalization to localization without a small parameter
• Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
• Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
• Spectral statistics of a minimal quantum glass model
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Quasiperiodicity hinders ergodic Floquet eigenstates
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• Many-body Localization in Clean Chains with Long-Range Interactions
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
• Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
• Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition
• Multifractality in the interacting disordered Tavis-Cummings model
• Power-Law Random Banded Matrix Ensemble as the Effective Model for Many-Body Localization Transition
• Investigating finite-size effects in random matrices by counting resonances
• Quantum transport efficiency in noisy random-removal and small-world networks
• Emergent multifractality in power-law decaying eigenstates
• Coherent Forward Scattering Peak and Multifractality
• Stability of quasicrystalline ultracold fermions to dipolar interactions
• Fate of Algebraic Many-Body Localization under driving
• Randomness-Assisted Exponential Hierarchies
• Critical dynamics of long-range quantum disordered systems
• More current with less particles due to power-law hopping
• Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
• Robust extended states in Anderson model on partially disordered random regular graphs
• Quantum Transports in Two-Dimensions with Long Range Hopping: Shielding, Localization and the Extended Isolated State
• Multifractality in monitored single-particle dynamics
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Anti-Drude Metal of Bosons
• Quantum Many-Body Scars in Few-Body Dipole-Dipole Interactions
• Refined cyclic renormalization group in Russian Doll model
• Tail states and unusual localization transition in low-dimensional Anderson model with power-law hopping
• Excitation transfer in disordered spin chains with long-range exchange interactions
• Unitary matrix integrals, symmetric polynomials, and long-range random walks
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
• Multifractality in high-dimensional graphs induced by correlated radial disorder
• The Wishart--Rosenzweig--Porter random matrix ensemble
• Localization and delocalization in one-dimensional systems with translation-invariant hopping
• Identifying mobility edge from finite temperature spectral form factor
• A multiscale reduced basis method for Schrödinger equation with multiscale and random potentials
• Localization and fractality in disordered Russian Doll model
• Replica approach to the generalized Rosenzweig-Porter model
• Many-body spectral transitions through the lens of the variable-range SYK2 model
• Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder
• Design Principles for Enhanced Quantum Transport with Site-Dependent Noise