Bose-Hubbard model on two-dimensional line graphs

TL;DR

This paper constructs a basis for the ground states of the Bose-Hubbard model on 2D line graphs, revealing localized particle states on cycles and identifying a critical filling factor for cycle close-packing.

Contribution

It introduces a novel basis construction for the ground states of the Bose-Hubbard model on line graphs of planar bipartite graphs at low fillings.

Findings

Particles are localized on non-intersecting cycles.

A critical filling factor is identified for close-packing of cycles.

The basis construction applies to finite 2-connected planar bipartite graphs.

Abstract

We construct a basis for the many-particle ground states of the positive hopping Bose-Hubbard model on line graphs of finite 2-connected planar bipartite graphs at sufficiently low filling factors. The particles in these states are localized on non-intersecting vertex-disjoint cycles of the line graph which correspond to non-intersecting edge-disjoint cycles of the original graph. The construction works up to a critical filling factor at which the cycles are close-packed.