# Pair Formation of Hard Core Bosons in Flat Band Systems

@article{Mielke2017PairFO,
title={Pair Formation of Hard Core Bosons in Flat Band Systems},
author={Andreas Mielke},
journal={Journal of Statistical Physics},
year={2017},
volume={171},
pages={679-695}
}
• A. Mielke
• Published 8 August 2017
• Physics
• Journal of Statistical Physics
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…
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## References

SHOWING 1-10 OF 34 REFERENCES

### Interacting bosons in two-dimensional flat band systems

• Physics
• 2015
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

### Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor

• Physics
• 2015
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

### Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands

• Physics
• 2013
To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $\pi$ flux, which has a flat band with a gap between the other band for noninteracting

### Haldane phase on the sawtooth lattice: Edge states, entanglement spectrum, and the flat band

• Physics
• 2016
Using density matrix renormalization group numerical calculations, we study the phase diagram of the half filled Bose-Hubbard system in the sawtooth lattice with strong frustration in the kinetic

### Geometry induced pair condensation

• Physics
• 2013
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

### Bose condensation in flat bands

• Physics
• 2010
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

### Boson localization and the superfluid-insulator transition.

• Physics
Physical review. B, Condensed matter
• 1989
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.

### Repulsively bound atom pairs in an optical lattice

• Physics
Nature
• 2006
These results exemplify the strong correspondence between the optical lattice physics of ultracold bosonic atoms and the Bose–Hubbard model—a link that is vital for future applications of these systems to the study of strongly correlated condensed matter and to quantum information.

### Exciton–polariton condensates with flat bands in a two-dimensional kagome lattice

• Physics
• 2012
Microcavity exciton–polariton condensates, as coherent matter waves, have provided a great opportunity to investigate hydrodynamic vortex properties, superfluidity and low-energy quantum state

### Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms

• Physics
Nature
• 2002
This work observes a quantum phase transition in a Bose–Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential, and can induce reversible changes between the two ground states of the system.