Localization of weakly interacting bosons in two dimensions: disorder vs lattice geometry effects

TL;DR

This study explores how disorder and lattice geometry influence localization phenomena in a 2D ultracold bosonic gas, revealing geometry-dependent localization behavior and the impact of disorder on energy spectra.

Contribution

It provides a comparative analysis of localization effects across different 2D lattice geometries using mean-field simulations, highlighting the role of lattice structure and coordination number.

Findings

Disorder induces a smooth localization transition in square and triangular lattices.

Honeycomb lattices show no localization at moderate disorder, partial localization at high disorder.

Disorder causes a continuous energy spectrum, replacing sharp peaks seen in clean systems.

Abstract

We investigate the effects of disorder and lattice geometry against localisation phenomena in a weakly interacting ultracold bosonic gas confined in a 2D optical lattice. The behaviour of the quantum fluid is studied at the mean-field level performing computational experiments, as a function of disorder strength for lattices of sizes similar to current experiments. Quantification of localisation, away from the Bose glass phase, was obtained directly from the stationary density profiles through a robust statistical analysis of the condensate component, as a function of the disorder amplitude. Our results show a smooth transition, or crossover, to localisation induced by disorder in square and triangular lattices. In contrast, associated to its larger tunneling amplitude, honeycomb lattices show absence of localisation for the same range of disorder strengths and same lattice amplitude, while also exhibiting partial localisation for large disorder amplitudes. We also conclude that the coordination number z have a partial influence on how fast this smooth transition occurs as the system size increases. Signatures of disorder are also found in the ground state energy spectrum, where a continuous distribution emerges instead of a distribution of sharp peaks proper to the system in the absence of disorder.