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.
16 pages, 14 figures
References in corpus (18)
- Direct observation of Anderson localization of matter-waves in a controlled disorder
- Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
- Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
- Topological Anderson Insulator
- Nearest neighbor tight binding models with an exact mobility edge in one dimension
- Photonic Topological Anderson Insulators
- Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
- Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
- Observation of tunable mobility edges in generalized Aubry-André lattices
- Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
- Flat Bands Under Correlated Perturbations
- Observation of interaction-induced mobility edge in a disordered atomic wire
- Localization problem of the quasiperiodic system with the spin orbit interaction
- Coherence and decoherence in the Harper-Hofstadter model
- Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices
- Enhanced transport of spin-orbit coupled Bose gases in disordered potentials
- Localization on a synthetic Hall cylinder
- Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator