Pair formation of hard core bosons in flat band systems

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.

16 pages, 8 figures

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Repulsively bound atom pairs in an optical lattice
• Bose condensation in flat bands
• Quantum liquid of repulsively bound pairs of particles in a lattice
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Low-energy behaviour of strongly-interacting bosons on a flat-banded lattice above the critical filling factor
• Haldane phase in the sawtooth lattice: Edge states, entanglement spectrum and the flat band
• Interacting bosons in two-dimensional flat band systems
• Hard-core bosons in flat band systems above the critical density

Cited by in corpus (8)

• Universal $d=1$ flatband generator from compact localized states
• Flatband generator in two dimensions
• The Rhombi-Chain Bose-Hubbard Model: geometric frustration and interactions
• Spectral Properties of Two Coupled Fibonacci Chains
• Mott Insulator-like Bose-Einstein Condensation in a Tight-Binding System of Interacting Bosons with a Flat Band
• Trapping Hard-Core Bosons in Flatband Lattices
• Dimers, trimers, tetramers, and other multimers in a multiband Bose-Hubbard model
• Localised pair formation in bosonic flat-band Hubbard models