Localised pair formation in bosonic flat-band Hubbard models

• Verfasst von: Fronk, Jacob [VerfasserIn]
• Verfasst von: Mielke, Andreas [VerfasserIn]
• Titel: Localised pair formation in bosonic flat-band Hubbard models
• Verf.angabe: Jacob Fronk, Andreas Mielke
• E-Jahr: 2021
• Jahr: 27 October 2021
• Umfang: 31 S.
• Fussnoten: Gesehen am 24.11.2021
• Titel Quelle: Enthalten in: Journal of statistical physics
• Ort Quelle: New York, NY [u.a.] : Springer Science + Business Media B.V., 1969
• Jahr Quelle: 2021
• Band/Heft Quelle: 185(2021), 2, Artikel-ID 14, Seite 1-31
• ISSN Quelle: 1572-9613
• DOI: doi:10.1007/s10955-021-02842-x
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1778916961
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Flat-band systems are ideal model systems to study strong correlations. In a large class of one or two dimensional bosonic systems with a lowest flat-band it has been shown that at a critical density the ground states are Wigner crystals. Under very special conditions it has been shown that pair formation occurs if one adds another particle to the system. The present paper extends this result to a much larger class of lattices and to a much broader region in the parameter space. Further, a lower bound for the energy gap between these pair states and the rest of the spectrum is established. The pair states are dominated by a subspace spanned by states containing a compactly localised pair. Overall, this strongly suggests localised pair formation in the ground states of the broad class of flat-band systems and rigorously proves it for some of the graphs in it, including the inhomogeneous chequerboard chain as well as two novel examples of regular two dimensional graphs. Physically, this means that the Wigner crystal remains intact if one adds a particle to it.