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 multiparticle spectrum. The proofs use a Gerschgorin type of argument for block diagonally dominant matrices. In certain onedimensional or treelike structures one can show that the pair is localised, for example in the chequerboard chain. For this onedimensional system with periodic boundary condition the energy band for the pair is flat, the pair is localised.
 Publication:

arXiv eprints
 Pub Date:
 August 2017
 arXiv:
 arXiv:1708.02508
 Bibcode:
 2017arXiv170802508M
 Keywords:

 Condensed Matter  Quantum Gases;
 Mathematical Physics
 EPrint:
 16 pages, 8 figures