Bose-Hubbard model on two-dimensional line 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.

9 pages, 5 figures, figures and conclusions updated

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Cited by in corpus (6)

• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Interacting bosons in two-dimensional flat band systems
• Pair formation of hard core bosons in flat band systems
• Particle Statistics, Frustration, and Ground-State Energy
• Hard-core bosons in flat band systems above the critical density
• Localised pair formation in bosonic flat-band Hubbard models