Renormalization to localization without a small parameter
arXiv:2001.06493 · doi:10.21468/SciPostPhys.8.4.049
Abstract
We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to the generality of this model usually called the Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena. We generalize the known Burin-Levitov renormalization group approach, formulate universal conditions sufficient for localization in such models and inspect a striking equivalence of the wave function spatial decay between Euclidean random matrices and translation-invariant long-range lattice models with a diagonal disorder.
arXiv comment22 pages, 7 figures, 55 references
References in corpus (43)
- Many-body localization edge in the random-field Heisenberg chain
- The Ergodic Side of the Many-Body Localization Transition
- Anderson localization on the Bethe lattice: non-ergodicity of extended states
- Multifractal Scalings across the Many-Body Localization Transition
- Non-equilibrium quantum magnetism in a dipolar lattice gas
- Multifractality and critical fluctuations at the Anderson transition
- One-dimensional quasicrystals with power-law hopping
- A random matrix model with localization and ergodic transitions
- Rare region effects and dynamics near the many-body localization transition
- Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
- Many-body localization and delocalization in large quantum chains
- Thouless energy and multifractality across the many-body localization transition
- Non-ergodic phases in strongly disordered random regular graphs
- Spectra of Euclidean Random Matrices
- Correlation-induced localization
- Scaling theory of the Anderson transition in random graphs: ergodicity and universality
- Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
- Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
- Statistics of eigenstates near the localization transition on random regular graphs
- Return probability for the Anderson model on the random regular graph
- Delocalized Glassy Dynamics and Many Body Localization
- Critical behavior at the localization transition on random regular graphs
- Duality in power-law localization in disordered one-dimensional systems
- Self-dual quasiperiodic systems with power-law hopping
- Two critical localization lengths in the Anderson transition on random graphs
- Sub-diffusion in the Anderson model on random regular graph
- Multifractality of wave functions on a Cayley tree: From root to leaves
- Non-Hermitian Euclidean random matrix theory
- Shielding and localization in presence of long range hopping
- Eigenvalue distributions of large Euclidean random matrices for waves in random media
- Anderson transition on the Bethe lattice: an approach with real energies
- Localization, anomalous diffusion and slow relaxations: a random distance matrix approach
- Multifractality without fine-tuning in a Floquet quasiperiodic chain
- Robustness of delocalization to the inclusion of soft constraints in long-range random models
- Quantum Levy flights and multifractality of dipolar excitations in a random system
- Mean-field model for the density of states of jammed soft spheres
- Emergent percolation length and localization in random elastic networks
- The Spectral Backbone of Excitation Transport in Ultra-Cold Rydberg Gases
- The effect of anisotropy of long-range hopping on localization in three-dimensional lattices
- Polarizability of electrically induced magnetic vortex plasma
- Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices
- Analysis of vibrational normal modes for Coulomb clusters
- Cooperative effects and photon localization in atomic gases: The two-dimensional case
Cited by in corpus (18)
- Multifractality meets entanglement: relation for non-ergodic extended states
- Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
- Non-ergodic delocalized phase with Poisson level statistics
- Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
- 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
- Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
- Emergent multifractality in power-law decaying eigenstates
- Investigating finite-size effects in random matrices by counting resonances
- Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry
- Beyond Fermi's golden rule with the statistical Jacobi approximation
- Single-particle localization in a two-dimensional Rydberg spin system
- 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
- Localization and fractality in disordered Russian Doll 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