Corpus ID: 220968755

Localised pair formation in bosonic flat-band Hubbard models

  title={Localised pair formation in bosonic flat-band Hubbard models},
  author={Jacob Fronk and A. Mielke},
  journal={arXiv: Mathematical Physics},
Using a generalised version of Gershgorin's circle theorem, rigorous boundaries on the energies of the lowest states of a broad class of line graphs above a critical filling are derived for hardcore bosonic systems. Also a lower boundary on the energy gap towards the next lowest states is established. Additionally, it is shown that the corresponding eigenstates are dominated by a subspace spanned by states containing a compactly localised pair and a lower boundary for the overlap is derived as… Expand
1 Citations

Figures and Tables from this paper

Mott Insulator-like Bose-Einstein Condensation in a Tight-Binding System of Interacting Bosons with a Flat Band
Hosho Katsura, 2, 3 Naoki Kawashima, Satoshi Morita, Akinori Tanaka, and Hal Tasaki Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, JapanExpand


Pair Formation of Hard Core Bosons in Flat Band Systems
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, theExpand
Interacting bosons in two-dimensional flat band systems
The Hubbard model of bosons on two dimensional lattices with a lowest flat band is discussed. In these systems there is a critical density, where the ground state is known exactly and can beExpand
Hard-core bosons in flat band systems above the critical density
Abstract We investigate the behaviour of hard-core bosons in one- and two-dimensional flat band systems, the chequerboard and the kagomé lattice and one-dimensional analogues thereof. TheExpand
Bose–Hubbard model on two-dimensional line graphs
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.Expand
Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor
Bosons interacting repulsively on a lattice with a flat lowest band energy dispersion may, at sufficiently small filling factors, enter into a Wigner-crystal-like phase. This phase is a consequenceExpand
Geometry induced pair condensation
We study a one-dimensional model of interacting bosons on a lattice with two flat bands. Regular condensation is suppressed due to the absence of a well defined minimum in the single particleExpand
Ferromagnetism in the Hubbard models with degenerate single-electron ground states.
  • Tasaki
  • Physics, Medicine
  • Physical review letters
  • 1992
This is the first time that a three-dimensional itinerant-electron system is proved to exhibit ferromagnetism in a finite range of the electron filling factor. Expand
d-wave superconductivity and pomeranchuk instability in the two-dimensional hubbard model
The flow of effective interactions and susceptibilities confirms the expected existence of a d-wave pairing instability driven by antiferromagnetic spin fluctuations and finds that strong forward scattering interactions develop which may lead to a Pomeranchuk instability breaking the tetragonal symmetry of the Fermi surface. Expand
Two theorems on the Hubbard model.
  • Lieb
  • Physics, Medicine
  • Physical review letters
  • 1989
The generalization given here yields, with ∣B∣ ≠ ∣A∣, the first provable example of itinerant electron ferromagnetism, and the theorems hold in all dimensions without even the necessity of a periodic lattice structure. Expand
Ferromagnetism in the Hubbard model on line graphs and further considerations
Let L(G) be the line graph of a graph G=(V,E). The Hubbard model on L(G) has ferromagnetic ground states with a saturated spin if the interaction is repulsive (U>0) and if the number of electrons NExpand