Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
arXiv:2001.04954 · doi:10.1103/PhysRevB.101.174203
Abstract
As opposed to random disorder, which localizes single-particle wave-functions in 1D at arbitrarily small disorder strengths, there is a localization-delocalization transition for quasi-periodic disorder in the 1D Aubry-André model at a finite disorder strength. On the single-particle level, many properties of the ground-state critical behavior have been revealed by applying a real-space renormalization-group scheme; the critical properties are determined solely by the continued fraction expansion of the incommensurate frequency of the disorder. Here, we investigate the many-particle localization-delocalization transition in the Aubry-André model with and without interactions. In contrast to the single-particle case, we find that the critical exponents depend on a Diophantine equation relating the incommensurate frequency of the disorder and the filling fraction which generalizes the dependence, in the single-particle spectrum, on the continued fraction expansion of the incommensurate frequency. This equation can be viewed as a generalization of the resonance condition in the commensurate case. When interactions are included, numerical evidence suggests that interactions may be irrelevant at at least some of these critical points, meaning that the critical exponent relations obtained from the Diophantine equation may actually survive in the interacting case.
arXiv comment14 pages, 8 figures
References in corpus (51)
- The density-matrix renormalization group in the age of matrix product states
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Many-body localization, thermalization, and entanglement
- Anderson localization of a non-interacting Bose-Einstein condensate
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- Topological States and Adiabatic Pumping in Quasicrystals
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- Fidelity approach to quantum phase transitions
- Direct observation of a localization transition in quasi-periodic photonic lattices
- Many-Body Localization in a Quasiperiodic System
- Nearest neighbor tight binding models with an exact mobility edge in one dimension
- Coupling Identical 1D Many-Body Localized Systems
- Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
- Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
- Two universality classes for the many-body localization transition
- Observation of many-body localization in a one-dimensional system with single-particle mobility edge
- From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
- Quench dynamics near a quantum critical point
- Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
- The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
- Flat Bands Under Correlated Perturbations
- Many body localization and quantum non-ergodicity in a model with a single-particle mobility edge
- Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
- Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
- Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion
- Interaction instability of localization in quasiperiodic systems
- Flatband Engineering of Mobility Edges
- Many-body delocalization dynamics in long Aubry-André quasiperiodic chains
- Anomalous transport in the Aubry-André-Harper model in isolated and open systems
- Localization of interacting fermions in the Aubry-Andre' model
- Transport properties across the many-body localization transition in quasiperiodic and random systems
- Detecting a many-body mobility edge with quantum quenches
- One-particle density matrix characterization of many-body localization
- Fractality in nonequilibrium steady states of quasiperiodic systems
- Critical quantum chaos and the one dimensional Harper model
- Kibble-Zurek mechanism with a single particle: dynamics of the localization-delocalization transition in the Aubry-André model
- Delocalization of weakly interacting bosons in a 1D quasiperiodic potential
- Fidelity Susceptibility in One-dimensional Disordered Lattice Models
- Universality and Quantum Criticality in Quasiperiodic Spin Chains
- Non-power-law universality in one-dimensional quasicrystals
- Interacting particles at a metal-insulator transition
- Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems
- Transitions Between Hall Plateaus and the Dimerization Transition of a Hubbard Chain
- Localization in interacting fermionic chains with quasi-random disorder
- Critical exponents of the disorder-driven superfluid-insulator transition in one-dimensional Bose-Einstein condensates
- Transport properties of one-dimensional interacting fermions in aperiodic potentials
- Localization of weakly interacting Bose gas in quasiperiodic potential
- Fidelity susceptibility of one-dimensional models with twisted boundary conditions
- Dense gaps and scaling relations in the interacting Aubry-Andre' model
- Multiple mobility edges in a 1D Aubry chain with Hubbard interaction in presence of electric field: Controlled electron transport
- Fractal x-ray edge problem at the critical point of the Aubry-André model
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- Many-body localization in a non-Hermitian quasi-periodic system
- Quantum Entanglement of Non-Hermitian Quasicrystals
- Dynamics of a quantum phase transition in the Aubry-André-Harper model with -wave superconductivity
- Quantum criticality and universality in the -wave paired Aubry-André-Harper model
- Quantum dynamics in the interacting Fibonacci chain
- Localization Driven Quantum Sensing
- Mean field theory of failed thermalizing avalanches
- Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems
- Critical and Topological Phases of Dimerized Kitaev Chain in Presence of Quasiperiodic Potential
- Stability of Weyl semimetals with quasiperiodic disorder
- A numerical study of the localization transition of Aubry-André type models
- Exploring unconventional quantum criticality in the p-wave-paired Aubry-André-Harper model
- Short-range interactions are irrelevant at the quasiperiodic-driven Luttinger Liquid to Anderson Glass transition
- Topological quantum optical states in quasiperiodic cold atomic chains
- Topological phonon polariton enhanced radiative heat transfer in bichromatic nanoparticle arrays mimicking Aubry-André-Harper model
- Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility
- Barriers to Macroscopic Superfluidity and Insulation in a 2D Aubry-André Model
- Non-equilibrium boundary driven quantum systems: models, methods and properties
- Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model
- Interaction-induced reentrance of Bose glass and quench dynamics of Bose gases in twisted bilayer and quasicrystal optical lattices
- Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
- Metallic-insulator phase transitions in the extended Harper model
- Characterizing the delocalized-localized Anderson phase transition based on the system's response to boundary conditions
- Effective Luttinger parameter and Kane-Fisher effect in quasiperiodic systems
- Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder
- Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe
- Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
- From generating functions to the geometric Binder cumulant
- Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux
- Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation