Pair formation of hard core bosons in flat band systems

TL;DR

This paper investigates the behavior of hard core bosons in flat band systems, revealing critical densities, Wigner crystal formations, and pair localization phenomena, with rigorous proofs and specific examples like the chequerboard chain.

Contribution

It provides a rigorous analysis of pair formation and localization in flat band systems, introducing new methods to describe ground states at critical densities.

Findings

Ground states are Wigner crystals below critical density.

Adding a particle creates a localized pair with a distinct energy band.

In certain structures, the pair's energy band is flat and the pair is localized.

Abstract

Hard core bosons in a large class of one or two dimensional flat band systems have an upper critical density, below which the ground states can be described completely. At the critical density, the ground states are Wigner crystals. If one adds a particle to the system at the critical density, the ground state and the low lying multi particle states of the system can be described as a Wigner crystal with an additional pair of particles. The energy band for the pair is separated from the rest of the multi-particle spectrum. The proofs use a Gerschgorin type of argument for block diagonally dominant matrices. In certain one-dimensional or tree-like structures one can show that the pair is localised, for example in the chequerboard chain. For this one-dimensional system with periodic boundary condition the energy band for the pair is flat, the pair is localised.