Edge-localized states in quantum one-dimensional lattices

TL;DR

This paper investigates edge-localized states in one-dimensional quantum lattice models, demonstrating their existence in bosonic and fermionic systems, and analyzing their properties through numerical and analytical methods.

Contribution

It introduces the study of edge-localized eigenstates in both bosonic and fermionic 1D lattice models, highlighting their characteristics and emergence with increasing particle number.

Findings

Edge states exist in Bose-Hubbard and spinless fermion models.

Localization characterized by spectral and eigenfunction analysis.

More complex edge states emerge as particle number increases.

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.