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arXiv:0902.3249 · Physical Review A

Edge-localized states in quantum one-dimensional lattices

Ricardo A. Pinto, Masudul Haque, Sergej Flach A

Published May 26, 2009• 47 citations
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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.

DOI
10.1103/physreva.79.052118

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We suggest that if a localized phase at nonzero temperature T>0T>0T>0 exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and TTT is very high. We show that in this high-TTT regime, the localization transition may be studied numerically through exact diagonalization of small systems. We obtain spectra for one-dimensional lattice models of interacting spinless fermions in a random potential. As expected, the spectral statistics of finite-size samples cross over from those of orthogonal random matrices in the diffusive regime at weak random potential to Poisson statistics in the localized regime at strong randomness. However, these data show deviations from simple one-parameter finite-size scaling: the apparent mobility edge ``drifts'' as the system's size is increased. Based on spectral statistics alone, we have thus been unable to make a strong numerical case for the presence of a many-body localized phase at nonzero TTT.
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