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We study the spectrum and eigenstates of the quantum discrete Bose-HubbardHamiltonian in a finite one-dimensional lattice containing two bosons. Theinteraction between the bosons leads to an algebraic localization of themodified extended states in the normal mode space of the noninteracting system.Weight functions of the eigenstates in the space of normal modes are computedby using numerical diagonalization and perturbation theory. We find thatstaggered states do not compactify in the dilute limit for large chains.Comment: 7 pages, 7 figures. Minor changes and additional comments. Acepted in  Physical Review

physical review. b, condensed matter and materials physics

Quantum<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>q</mml:mi></mml:math>-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

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