Duality breaking, mobility edges, and the connection between topological Aubry-André and quantum Hall insulators in atomic wires with fermions
arXiv:2501.13190 · doi:10.1103/PhysRevA.111.023322
Abstract
It is well known that the Aubry-Andr{é} model lacks mobility edges due to its energy-independent self-duality but may exhibit edge states. When duality is broken, we show that mobility regions arise and non-trivial topological phases emerge. By varying the degree of duality breaking, we identify mobility regions and establish a connection between Aubry-Andr{é} atomic wires with fermions and quantum Hall systems for a family of Hamiltonians that depends on the relative phase of laser fields, viewed as a synthetic dimension. Depending on the filling factor and the degree of duality breaking, we find three classes of non-trivial phases: conventional topological insulator, conventional topological Aubry-Andr{é} insulator, and unconventional (hybrid) topological Aubry-Andr{é} insulator. Finally, we discuss appropriate Chern numbers that illustrate the classification of topological phases of localized fermions in atomic wires.
arXiv comment16 pages, 14 figures
References in corpus (42)
- Topological Order and the Quantum Spin Hall Effect
- Experimental realisation of the topological Haldane model
- 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
- Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
- Anderson localization and nonlinearity in one dimensional disordered photonic lattices
- Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
- Topological Anderson Insulator
- Statistical Signatures of Photon Localization
- Observation of the critical regime near Anderson localization of light
- Theory of the topological Anderson insulator
- Three-dimensional localization of ultracold atoms in an optical disordered potential
- Three-Dimensional Anderson Localization of Ultracold Matter
- Nearest neighbor tight binding models with an exact mobility edge in one dimension
- Photonic Topological Anderson Insulators
- 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
- Time-reversal-symmetry-broken quantum spin Hall effect
- Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
- Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
- One dimensional quasiperiodic mosaic lattice with exact mobility edges
- Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle
- Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
- Observation of tunable mobility edges in generalized Aubry-André lattices
- Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
- Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
- Flat Bands Under Correlated Perturbations
- Extracting the Chern number from the dynamics of a Fermi gas: Implementing a quantum Hall bar for cold atoms
- Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor
- Observation of interaction-induced mobility edge in a disordered atomic wire
- Phase Diagram for Quantum Hall Bilayers at
- Observation of two-dimensional Anderson localisation of ultracold atoms
- Chern numbers hiding in time-of-flight images
- Anderson Localization of cold atomic gases with effective spin-orbit interaction in a quasiperiodic optical lattice
- Localization problem of the quasiperiodic system with the spin orbit interaction
- Anderson transition of cold atoms with synthetic spin-orbit coupling in two-dimensional speckle potentials
- Coherence and decoherence in the Harper-Hofstadter model
- Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices
- Localization on a synthetic Hall cylinder
- Enhanced transport of spin-orbit coupled Bose gases in disordered potentials
- Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator
- Chern number spectrum of ultra-cold fermions in optical lattices tuned independently via artificial magnetic, Zeeman and spin-orbit fields