Unconventional edge states in a two-leg ladder
arXiv:2407.05888 · doi:10.1088/1367-2630/ad5bf9
Abstract
Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other methods for inducing somewhat localized states in elementary lattice models have been historically much less studied. Here we show how edge states can emerge within a simple two-leg ladder of coupled harmonic oscillators, where it is important to include interactions beyond those at the nearest neighbour range. Remarkably, depending upon the interplay between the coupling strength along the rungs of the ladder and the next-nearest neighbour coupling strength along one side of the ladder, edge states can indeed appear at particular energies. In a wonderful manifestation of a type of bulk-edge correspondence, these edge state energies correspond to the quantum number for which additional stationary points appear in the continuum bandstructure of the equivalent problem studied with periodic boundary conditions. Our theoretical results are relevant to a swathe of classical or quantum lattice model simulators, such that the proposed edge states may be useful for applications including waveguiding in metamaterials and quantum transport.
23 pages, 11 figures
References in corpus (49)
- Topological Insulators
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Random Matrix Theories in Quantum Physics: Common Concepts
- Localization of interacting fermions at high temperature
- Ultrastrong coupling regimes of light-matter interaction
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Observation of the Meissner effect with ultracold atoms in bosonic ladders
- Anomalous diffusion and Griffiths effects near the many-body localization transition
- Microscopy of the interacting Harper-Hofstadter model in the few-body limit
- Interference traps waves in open system: Bound states in the continuum
- Programmable Interactions and Emergent Geometry in an Atomic Array
- Direct observation of chiral currents and magnetic reflection in atomic flux lattices
- Properties of lightly doped t-J two-leg ladders
- Meissner effect in a bosonic ladder
- Critical and bicritical properties of Harper's equation with next nearest neighbor coupling
- Bound states in the continuum in photonic structures
- Reconfigurable topological phases in next-nearest-neighbor coupled resonator lattices
- Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: Swimming against the tide
- Critical properties of the Anderson localization transition and the high dimensional limit
- Theory of Bosons in two-leg ladders with large magnetic fields
- Topology and interactions in the photonic Creutz and Creutz-Hubbard ladders
- Optical control of synchronous phases in a programmable polariton cell
- Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs
- Observation of thermalization and information scrambling in a superconducting quantum processor
- Mobility edge and multifractality in a periodically driven Aubry-André model
- Programmable large-scale simulation of bosonic transport in optical synthetic frequency lattices
- Non-Local Phononic Crystals for Dispersion Customization and Undulation-point Dynamics
- Extreme Spatial Dispersion in Nonlocally-Resonant Elastic Metamaterials
- Mott-Superfluid transition in bosonic ladders
- Disorder-enhanced transport in a chain of lossy dipoles strongly coupled to cavity photons
- Anomalous multifractality in quantum chains with strongly correlated disorder
- Level Repulsion and Dynamics in the Finite One-Dimensional Anderson Model
- Breakdown of Conventional Winding Number Calculation in One-Dimensional Lattices with Interactions Beyond Nearest Neighbors
- From few- to many-body quantum systems
- Edge states of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange
- Unconventional next nearest neighbor resonance coupling and states flipping mechanism in degenerate optical microcavities
- Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: engineering of mobility gaps and multifractal states
- Polaritonic Tamm states induced by cavity photons
- Finite wave vector pairing in doped two-leg ladders
- Exceptional points in oligomer chains
- Cluster Gutzwiller study of Bose-Hubbard ladder: ground-state phase diagram and many-body Landau-Zener dynamics
- Doublons, topology and interactions in a one-dimensional lattice
- Next nearest neighbour coupling with spinor polariton condensates
- Quantum topology in the ultrastrong coupling regime
- Screening nearest-neighbor interactions in networks of exciton-polariton condensates through spin orbit coupling
- Multiple polaritonic edge states in a Su-Schrieffer-Heeger chain strongly coupled to a multimode cavity
- The Effect of Next-Nearest Neighbour Hopping in the One, Two, and Three Dimensional Holstein Model
- Quantum phases of constrained bosons on a two-leg Bose-Hubbard ladder
- Quantum phases of the biased two-chain-coupled Bose-Hubbard Ladder