Localised Pair Formation in Bosonic Flat-Band Hubbard Models

  title={Localised Pair Formation in Bosonic Flat-Band Hubbard Models},
  author={Jacob Fronk and Andreas Mielke},
  journal={Journal of Statistical Physics},
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… 
1 Citations

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, Japan



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, the

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 consequence

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 be

Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons

In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. Main emphasis is made on recent developments which include results

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. The

Bose condensation in flat bands

We derive effective Hamiltonians for lattice bosons with strong geometrical frustration of the kinetic energy by projecting the interactions on the flat lowest Bloch band. Specifically, we consider

Two theorems on the Hubbard model.

  • Lieb
  • Mathematics
    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.

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 particle

Boson localization and the superfluid-insulator transition.

It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed.

REVIEW ARTICLE: The Hubbard model - an introduction and selected rigorous results

The Hubbard model is a `highly oversimplified model' for electrons in a solid which interact with each other through extremely short-ranged repulsive (Coulomb) interaction. The Hamiltonian of the