Relative and center-of-mass motion in the attractive Bose-Hubbard model

TL;DR

This paper numerically investigates the attractive Bose-Hubbard model, revealing that low-energy states are superpositions of localized particle clusters, which explain the energy spectrum through their center-of-mass and internal excitations.

Contribution

It introduces a numerical approach to analyze few-particle states, showing they form translational superpositions of localized clusters, providing insight into the model's energy spectrum.

Findings

Low-energy states are superpositions of localized particle clusters.

Compact states break translational symmetry.

Center-of-mass and internal excitations explain the energy spectrum.

Abstract

We present first-principle numerical calculations for few particle solutions of the attractive Bose-Hubbard model with periodic boundary conditions. We show that the low-energy many-body states found by numerical diagonalization can be written as translational superposition states of compact composite systems of particles. These compact states break the translational symmetry of the problem and their center-of-mass and internal excitations offer simple explanations of the energy spectrum of the full model.