Quantum q-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

TL;DR

This paper investigates the spectral properties and eigenstates of a finite Bose-Hubbard chain with two interacting bosons, revealing algebraic localization effects and the behavior of staggered states in large systems.

Contribution

It provides a detailed analysis of quantum q-breathers in a finite Bose-Hubbard model, combining numerical and perturbative methods to uncover localization phenomena.

Findings

Interaction causes algebraic localization in eigenstates.

Staggered states do not become localized in the dilute limit for large chains.

Eigenstate weight functions are characterized in normal mode space.

Abstract

We study the spectrum and eigenstates of the quantum discrete Bose-Hubbard Hamiltonian in a finite one-dimensional lattice containing two bosons. The interaction between the bosons leads to an algebraic localization of the modified extended states in the normal mode space of the noninteracting system. Weight functions of the eigenstates in the space of normal modes are computed by using numerical diagonalization and perturbation theory. We find that staggered states do not compactify in the dilute limit for large chains.