Journal of Statistical Physics

, Volume 171, Issue 4, pp 679–695 | Cite as

Pair Formation of Hard Core Bosons in Flat Band Systems

  • Andreas Mielke


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.


Hubbard model Hard-core bosons Flat-bands Line-graphs Pair formation 



I wish to thank Moritz Drescher for fruitful discussion, for reading the manuscript, and for several helpful remarks.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversity of HeidelbergHeidelbergGermany

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