Boundary effects on quantum q-breathers in a Bose-Hubbard chain

TL;DR

This paper studies how boundary conditions affect the spectral properties and eigenstates of a two-boson Bose-Hubbard chain, revealing boundary-induced effects on quantum q-breathers and bound states.

Contribution

It introduces a detailed analysis of boundary effects on quantum q-breathers in a Bose-Hubbard chain with two bosons, combining perturbation theory and numerical methods.

Findings

Identification of rims in normal-mode space where eigenstate weights concentrate

Algebraic decay of weights along and off the rims

Boundary effects influence the formation of two-boson bound states

Abstract

We investigate the spectrum and eigenstates of a Bose-Hubbard chain containing two bosons with fixed boundary conditions. In the noninteracting case the eigenstates of the system define a two-dimensional normal-mode space. For the interacting case weight functions of the eigenstates are computed by perturbation theory and numerical diagonalization. We identify paths in the two-dimensional normal-mode space which are rims for the weight functions. The decay along and off the rims is algebraic. Intersection of two paths (rims) leads to a local enhancement of the weight functions. We analyze nonperturbative effects due to the degeneracies and the formation of two-boson bound states.