Emergent multifractality in power-law decaying eigenstates
arXiv:2501.17242 · doi:10.1103/bnr3-5dcw
Abstract
Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally believed to be a critical phenomenon and fragile to random perturbations. In this work, we propose a set of generic principles based on the power-law decay of the eigenstates which allow us to distinguish a fractal phase from a genuine multifractal phase. We demonstrate the above principles in a 1d tight-binding model with inhomogeneous nearest-neighbor hopping that can be mapped to the standard quantum harmonic oscillator via energy-coordinate duality. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions which are in agreement with numerical simulations.
4.25 pages, 3 figures, 106 references + 3 pages in Appendices
References in corpus (75)
- Anderson Transitions
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Many-body localization, thermalization, and entanglement
- The many-body localization phase transition
- Perfect state transfer in quantum spin networks
- Many-body localization edge in the random-field Heisenberg chain
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- Many-body localization: an introduction and selected topics
- Matrix Models for Beta Ensembles
- A Universal Operator Growth Hypothesis
- Mirror Inversion of Quantum States in Linear Registers
- Multifractal Scalings across the Many-Body Localization Transition
- Multifractality and critical fluctuations at the Anderson transition
- Eigenfunction fractality and pseudogap state near superconductor-insulator transition
- Fractal superconductivity near localization threshold
- Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
- A random matrix model with localization and ergodic transitions
- Dynamics at the Many-Body Localization Transition
- Quantum state transfer via the ferromagnetic chain in a spatially modulated field
- Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
- Quantum breakdown of superconductivity in low-dimensional materials
- Experimental Perfect Quantum State Transfer
- Correlation-induced localization
- Many-Body Localization in the Age of Classical Computing
- Phase diagram of a non-Abelian Aubry-André-Harper model with -wave superfluidity
- Electron wavepacket propagation and entanglement in a chain of coupled quantum dots
- Enhancement of superconductivity by Anderson localization
- Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
- Rare thermal bubbles at the many-body localization transition from the Fock space point of view
- From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
- Many-body localization transition with power-law interactions: Statistics of eigenstates
- Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
- A disorder-enhanced quasi-one-dimensional superconductor
- Duality in power-law localization in disordered one-dimensional systems
- Dynamical phases in a "multifractal" Rosenzweig-Porter model
- Eigenfunction distribution for the Rosenzweig-Porter model
- Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
- The Lévy-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
- Stability of topological edge states under strong nonlinear effects
- Non-Ergodic Delocalization in the Rosenzweig-Porter Model
- Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach
- Robustness of delocalization to the inclusion of soft constraints in long-range random models
- Non-ergodic extended states in the SYK model
- Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems
- Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape
- Emergent fractal phase in energy stratified random models
- Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime
- Non-ergodic delocalized phase with Poisson level statistics
- Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
- Extreme statistics of complex random and quantum chaotic states
- Multifractality and self-averaging at the many-body localization transition
- High values of disorder-generated multifractals and logarithmically correlated processes
- The effect of anisotropy of long-range hopping on localization in three-dimensional lattices
- Dynamical quantum ergodicity from energy level statistics
- Level Repulsion and Dynamics in the Finite One-Dimensional Anderson Model
- 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
- Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
- Phase coherence in tight-binding models with nonrandom long-range hopping
- Anisotropy-mediated reentrant localization
- Renormalization to localization without a small parameter
- The Phase Transition in the Ultrametric Ensemble and Local Stability of Dyson Brownian Motion
- Analytic solution of the resolvent equations for heterogeneous random graphs: spectral and localization properties
- Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
- Chaos due to symmetry-breaking in deformed Poisson ensemble
- Anatomy of the eigenstates distribution: a quest for a genuine multifractality
- Robust non-ergodicity of ground state in the ensemble
- Dynamical Signatures of Chaos to Integrability Crossover in Generalized Random Matrix Ensembles
- Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
- Quantum multifractality as a probe of phase space in the Dicke model
- Multifractality and statistical localization in highly heterogeneous random networks
- Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
- Effect of Hilbert space truncation on Anderson localization