Effective delocalization in the one-dimensional Anderson model with stealthy disorder

Abstract

We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical transparency properties of stealthy hyperuniform layered media, we compute the localization length using a perturbative expansion of the self-energy. We find that, for fixed energy and small but finite disorder strength $W$, there exists for any finite length system a range of stealthiness $\chi$ for which the localization length exceeds the system size. This kind of "effective delocalization" is the result of the novel kind of correlated disorder that spans a continuous range of length scales, a defining characteristic of stealthy systems. Unlike uncorrelated disorder, for which the localization length $\xi$ scales as $W^{-2}$ to leading order for small W, the leading order terms in the perturbation expansion of $\xi$ for stealthy disordered systems vanish identically for a progressively large number of terms as $\chi$ increases such that $\xi$ scales as $W^{-2n}$ with arbitrarily large $n$. Moreover, we support our analytical results with numerical simulations. Our results introduce stealthy disorder into quantum tight-binding models and show that enforcing a low-$k$ spectral gap markedly alters the scattering landscape, enabling localization lengths that exceed the system size at fixed disorder strength. Since this mechanism relies only on the spectral properties of the disorder, it carries over directly to photonic and phononic wave systems.

7 + 4 pages, 5 figures

References in corpus (49)

• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Anderson localization of a non-interacting Bose-Einstein condensate
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Anderson localization and nonlinearity in one dimensional disordered photonic lattices
• Many-body localization in a quantum simulator with programmable random disorder
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Integrals of motion in the Many-Body localized phase
• Hyperuniform States of Matter
• Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
• Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem
• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• How a well-adapted immune system is organized
• Anderson localization on random regular graphs
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• From Anderson localization on Random Regular Graphs to Many-Body localization
• One-dimensional Anderson localization in certain correlated random potentials
• Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition
• Return probability for the Anderson model on the random regular graph
• Optical cavities and waveguides in hyperuniform disordered photonic solids
• Critical properties of the Anderson localization transition and the high dimensional limit
• Eigenfunction entropy and spectral compressibility for critical random matrix ensembles
• Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
• The many-body localized phase of the quantum random energy model
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
• Universality in Anderson localization on random graphs with varying connectivity
• Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases
• Anderson localization of matter waves in tailored disordered potentials
• Effective Electromagnetic Wave Properties of Disordered Stealthy Hyperuniform Layered Media Beyond the Quasistatic Regime
• Dimensional Dependence of Critical Exponent of the Anderson Transition in the Orthogonal Universality Class
• Renormalization Group Analysis of the Anderson Model on Random Regular Graphs
• Uncovering Multiscale Order in the Prime Numbers via Scattering
• Effective Elastic Wave Characteristics of Composite Media
• Quantum criticality in Ising chains with random hyperuniform couplings
• Investigating finite-size effects in random matrices by counting resonances
• Dynamical properties of particulate composites derived from ultradense stealthy hyperuniform sphere packings
• Renormalization group for Anderson localization on high-dimensional lattices
• Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain
• Scaling analysis and renormalization group on the mobility edge in the quantum random energy model
• Localization Transition for Interacting Quantum Particles in Colored-Noise Disorder

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