Edge-localized states in quantum one-dimensional lattices
arXiv:0902.3249 · doi:10.1103/PhysRevA.79.052118
Abstract
In one-dimensional quantum lattice models with open boundaries, we find and study localization at the lattice edge. We show that edge-localized eigenstates can be found in both bosonic and fermionic systems, specifically, in the Bose-Hubbard model with on-site interactions and in the spinless fermion model with nearest-neighbor interactions. We characterize the localization through spectral studies via numerical diagonalization and perturbation theory, through considerations of the eigenfunctions, and through the study of explicit time evolution. We concentrate on few-particle systems, showing how more complicated edge states appear as the number of particles is increased.
9 pages, 12 figures
References in corpus (15)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Cold bosonic atoms in optical lattices
- Discrete Breathers
- Repulsively bound atom pairs in an optical lattice
- Observation of surface gap solitons in semi-infinite waveguide arrays
- Quantum Lattice Solitons
- Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays
- Quantum Breathers in a Nonlinear Lattice
- Discrete surface solitons in semi-infinite binary waveguide arrays
- Quantum signatures of breather-breather interactions
- Relaxation channels of two-vibron bound states in α-helix proteins
- Discrete surface solitons in two-dimensional anisotropic photonic lattices
- Stability of quantum breathers
- Quantum q-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons
- Structure and time-dependence of quantum breathers
Cited by in corpus (29)
- Topological edge states of interacting photon pairs emulated in a topolectrical circuit
- Two-body physics in the Su-Schrieffer-Heeger model
- Topological edge states of bound photon pairs
- Dynamics and Transport at the Threshold of Many-Body Localization
- Interaction-induced topological properties of two bosons in flat-band systems
- Interaction-induced two-photon edge states in extended Hubbard model realized in a cavity array
- Topological bound states in interacting Su-Schrieffer-Heeger rings
- Edge-locking and quantum control in highly polarized spin chains
- Interaction-induced topological states of photon pairs
- Raise and fall of a bright soliton in an optical lattice
- Quasi-soliton scattering in quantum spin chains
- Beyond hard-core bosons in transmon arrays
- Open XXZ chain and boundary modes at zero temperature
- Bose-Hubbard ladder subject to effective magnetic field: quench dynamics in a harmonic trap
- Repulsive to attractive interaction quenches of 1D Bose gas in a harmonic trap
- NOON States via Quantum Walk of Bound Particles
- Simulation of two-boson bound states using arrays of driven-dissipative coupled linear optical resonators
- Majorana representation of adiabatic and superadiabatic processes in three-level systems
- Bethe ansatz description of edge-localization in the open-boundary XXZ spin chain
- Fine structures in the spectrum of the open-boundary Heisenberg chain at large anisotropies
- Phase diagram of two-component dipolar fermions in one-dimensional optical lattices
- Efficiency of fermionic quantum distillation
- Exceptional points for photon pairs bound by nonlinear dissipation in cavity arrays
- Edge states of photon pairs in cavity arrays with spatially modulated nonlinearity
- Soliton versus single photon quantum dynamics in arrays of superconducting qubits
- Floquet engineering of edge states in the presence of staggered potential and interactions
- Surface states in defect-free polyatomic lattices described by a tight-binding model
- Supercorrelated decay in a quasiperiodic nonlinear waveguide: From Markovian to non-Markovian transitions
- New perspective on symmetry breaking in a clean antiferromagnetic chain: Spin-selective transport and NDR phenomenon