Robustness of delocalization to the inclusion of soft constraints in long-range random models

Abstract

Motivated by the constrained many-body dynamics, the stability of the localization-delocalization properties to the inclusion of the soft constraints is addressed in random matrix models. These constraints are modeled by correlations in long-ranged hopping with Pearson correlation coefficient different from zero or unity. Counterintuitive robustness of delocalized phases, both ergodic and (multi)fractal, in these models is numerically observed and confirmed by the analytical calculations. First, matrix inversion trick is used to uncover the origin of such robustness. Next, to characterize delocalized phases a method of eigenstate calculation, sensitive to correlations in long-ranged hopping terms, is developed for random matrix models and approved by numerical calculations and previous analytical ansatz. The effect of the robustness of states in the bulk of the spectrum the inclusion of to soft constraints is generally discussed for single-particle and many-body systems.

arXiv comment10 pages, 5 figures, 94 references + 5 pages of Appendices

References in corpus (67)

• Probing many-body dynamics on a 51-atom quantum simulator
• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quantum many-body scars
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Many-body Localization with Dipoles
• Signatures of integrability in the dynamics of Rydberg-blockaded chains
• A random matrix model with localization and ergodic transitions
• Many-body localization dynamics from gauge invariance
• Dynamics at the Many-Body Localization Transition
• Localization in fractonic random circuits
• Correlation-induced localization
• 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
• Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance and out-of-time-ordered correlator
• 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 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
• Duality in power-law localization in disordered one-dimensional systems
• Transitions toward Quantum Chaos: with Supersymmetry from Poisson to Gauss
• Eigenstate Thermalization, Random Matrix Theory and Behemoths
• Eigenfunction distribution for the Rosenzweig-Porter model
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• 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
• 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
• Multifractality without fine-tuning in a Floquet quasiperiodic chain
• Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
• Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities
• Power-law decay exponents: a dynamical criterion for predicting thermalization
• Non-ergodic extended states in the SYK model
• Emergent locality in systems with power-law interactions
• Spectral diffusion and scaling of many-body delocalization transitions
• 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
• Virial expansion for almost diagonal random matrices
• 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
• Supersymmetry Approach to Almost Diagonal Random Matrices
• The effect of anisotropy of long-range hopping on localization in three-dimensional lattices
• Spread of wave packets in disordered hierarchical lattices
• Algebraic Localization from Power-Law Interactions in Disordered Quantum Wires
• Anderson localization on a simplex
• Phase coherence in tight-binding models with nonrandom long-range hopping
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• The Phase Transition in the Ultrametric Ensemble and Local Stability of Dyson Brownian Motion
• T-duality in supersymmetric theory of disordered quantum systems
• Support set of random wave-functions on the Bethe lattice
• Efficient population transfer via non-ergodic extended states in quantum spin glass
• Nonequilibrium many-body quantum dynamics: from full random matrices to real systems

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• Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
• 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
• Multifractality meets entanglement: relation for non-ergodic extended states
• Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Emergent fractal phase in energy stratified random models
• Non-ergodic delocalized phase with Poisson level statistics
• Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
• Flat-band-based multifractality in the all-band-flat diamond chain
• 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
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Anisotropy-mediated reentrant localization
• Renormalization to localization without a small parameter
• Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
• Quasiperiodicity hinders ergodic Floquet eigenstates
• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
• Many-body Localization in Clean Chains with Long-Range Interactions
• Emergent multifractality in power-law decaying eigenstates
• Modelling equilibration of local many-body quantum systems by random graph ensembles
• Robust extended states in Anderson model on partially disordered random regular graphs
• Fractal states of the Schwinger model
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Excitation transfer in disordered spin chains with long-range exchange interactions
• Refined cyclic renormalization group in Russian Doll model
• Anderson localisation in spatially structured random graphs
• Localization and fractality in disordered Russian Doll model
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder
• Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking