Hard-core bosons in flat band systems above the critical density

Drescher, Moritz; Mielke, Andreas

doi:10.1140/epjb/e2017-80218-1

Cited by 6 publications

(26 citation statements)

References 30 publications

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“…This result is relevant for recent works on the Creutz ladder [5,24,25,43] where both bosonic and fermionic Hubbard models have been considered. We note also that in a recent work by Drescher and Mielke [46] similar local conserved quantities associated to graph automorphisms have been found in a lattice Hamiltonian where only some bands are perfectly flat. In this case the conserved quantities seem not to be constructed from intertwining operators that perform a Φ 0 /2-flux insertion.…”

Section: B Conserved Quantitiessupporting

confidence: 81%

“…Second it emphasizes the connection between these symmetries and canonical transformations built from graph automorphisms. The connection between graph theory and flat band physics has a long history [47][48][49][50] and recent results [46,51] indicate that much remains to be done in this direction. Moreover it is clear that our results apply regardless of particle statistics.…”

Section: Discussionmentioning

confidence: 99%

“…[5], we use here the convention that the interaction parameter U can be both positive (repulsive case) or negative (attractive case). In order to expand the projected interaction (46) in terms of the operators in the Wannier basis it is convenient to introduce two families of (pseudo-)spin operators. One family of operators encodes the spin degree of freedom of localized single particles in the Wannier orbitals of the lowest band…”

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confidence: 99%

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Preformed pairs in flat Bloch bands

et al. 2018

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In a flat Bloch band the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in the presence of interactions is a challenging question because a flat dispersion usually leads to highly correlated ground states. Here we compute numerically the ground state energy of lattice models with completely flat band structure in a ring geometry in the presence of an attractive Hubbard interaction. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum Φ0/2 = hc/(2e) period, indicating that only bound pairs of particles with charge 2e are propagating, while single quasiparticles with charge e remain localized. For some one dimensional lattice models we show analytically that in fact the whole many-body spectrum has the same periodicity. Our analytical arguments are valid for both bosons and fermions, for generic interactions respecting some symmetries of the lattice and at arbitrary temperatures. Moreover for the same one dimensional lattice models we construct an extensive number of exact conserved quantities. These conserved quantities are associated to the occupation of localized single quasiparticle states and force the single-particle propagator to vanish beyond a finite range. Our results suggest that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state.

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Section: B Conserved Quantitiessupporting

confidence: 81%

Section: Discussionmentioning

confidence: 99%

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confidence: 99%

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Preformed pairs in flat Bloch bands

et al. 2018

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“…They appear for a sufficiently strong repulsive interaction as dynamically stable excited states. More recently, pair formation was proposed in the ground state of the bosonic Hubbard model in some special onedimensional lattice structures [29,32,25,27,10,6]. The pair formation occurring here is a collective effect and is caused by the interplay between the repulsive interaction and the movement of the particles in these lattice structures.…”

Section: Introductionmentioning

confidence: 92%

“…In the present paper we give a rigorous proof for pair formation in a large class of flat band structures. The class contains as examples the chequerboard chain [27,6] and its two-dimensional analogue, the chequerboard lattice. To our knowledge this is the first proof of pair formation in two-dimensional lattice structures with flat bands.…”

Section: Introductionmentioning

confidence: 99%

Pair Formation of Hard Core Bosons in Flat Band Systems

Mielke

2018

J Stat Phys

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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.

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Localised Pair Formation in Bosonic Flat-Band Hubbard Models

Fronk

Mielke

2021

J Stat Phys

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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.

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Hard-core bosons in flat band systems above the critical density

Cited by 6 publications

References 30 publications

Preformed pairs in flat Bloch bands

Preformed pairs in flat Bloch bands

Pair Formation of Hard Core Bosons in Flat Band Systems

Localised Pair Formation in Bosonic Flat-Band Hubbard Models

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