# Hard-core bosons in flat band systems above the critical density

## TL;DR

This paper studies hard-core bosons in flat band systems, revealing that above a critical density, particles form localized pairs, with exact results in 1D and indicative behavior in 2D.

## Contribution

It provides exact solutions for 1D systems and variational insights for 2D systems, demonstrating pair formation and localization above the critical density.

## Key findings

- Particles form localized pairs above the critical density
- Exact results obtained for 1D systems
- Variational results suggest similar behavior in 2D systems

## Abstract

We investigate the behaviour of hard-core bosons in one- and two-dimensional flat band systems, the chequerboard and the kagom\'e lattice and one-dimensional analogues thereof. The one dimensional systems have an exact local reflection symmetry which allows for exact results. We show that above the critical density an additional particle forms a pair with one of the other bosons and that the pair is localised. In the two-dimensional systems exact results are not available but variational results indicate a similar physical behaviour.