Edge-localized states in quantum one-dimensional lattices

Details Edge-localized states in quantum one-dimensional lattices Edge-localized states in quantum one-dimensional lattices

2009-02-18

arxiv.org/abs/0902.3249v1

Phys. Rev. A 79, 052118 (2009)

Physics

Condensed Matter

Other Condensed Matter

9 pages, 12 figures

Scientific paper

10.1103/PhysRevA.79.052118

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.

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