Correlation versus commensurability effects for finite bosonic systems in one-dimensional lattices

TL;DR

This paper studies how few-boson systems in finite one-dimensional traps transition from uncorrelated to fermionized states, revealing localization, fragmentation, and density modulations through exact numerical methods.

Contribution

It provides a comprehensive analysis of correlation and commensurability effects in finite bosonic systems across the interaction spectrum using the Multi-Configurational Time-Dependent Hartree method.

Findings

Localization increases with interaction strength for commensurate fillings.

On-site repulsion causes density fragmentation beyond Bose-Hubbard model predictions.

Incommensurate particles lead to incomplete localization and density modulations.

Abstract

We investigate few-boson systems in finite one-dimensional multi-well traps covering the full interaction crossover from uncorrelated to fermionized particles. Our treatment of the ground state properties is based on the numerically exact Multi-Configurational Time-Dependent Hartree method. For commensurate filling we trace the fingerprints of localisation, as the interaction strength increases, in several observables like reduced density matrices, fluctuations and momentum distribution. For filling factor larger than one we observe on-site repulsion effects in the densities and fragmentation of particles beyond the validity of the Bose-Hubbard model upon approaching the Tonks-Girardeau limit. The presence of an incommensurate fraction of particles induces incomplete localisation and spatial modulations of the density profiles, taking into account the finite size of the system.