Interacting bosons in two-dimensional flat band systems

TL;DR

This paper explores the behavior of interacting bosons in two-dimensional flat band systems, revealing how particle interactions lead to charge density waves, condensation, or pairing depending on density and lattice structure.

Contribution

It provides an exact ground state solution at a critical density and analyzes the mechanisms behind particle delocalization, condensation, and pairing in flat band bosonic systems.

Findings

Exact ground state at critical density as a charge density wave

Delocalization and condensation above critical filling

Pair formation at strong interactions, e.g., on chequerboard lattice

Abstract

The Hubbard model of bosons on two dimensional lattices with a lowest flat band is discussed. In these systems there is a critical density, where the ground state is known exactly and can be represented as a charge density wave. Above this critical filling, depending on the lattice structure and the interaction strength, the additional particles are either delocalised and condensate in the ground state, or they form pairs. Pairs occur at strong interactions, e.g., on the chequerboard lattice. The general mechanism behind this phenomenon is discussed.