Interaction Induced Delocalization for Two Particles in a Periodic Potential

Vidal, Julien; Douçot, Benoît; Mosseri, Rémy; Butaud, P.

doi:10.1103/physrevlett.85.3906

Cited by 172 publications

(204 citation statements)

References 12 publications

(16 reference statements)

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“…Flat bands add a very intriguing flavor to the dynamics, as atoms occupying such bands are essentially immobile, and allow us to contrast bosons and fermions. In a magnetic field, such immobility means localization in a so-called Aharonov-Bohm cage [21,22].…”

Section: Introductionmentioning

confidence: 99%

Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices

2013

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The difference between boson and fermion dynamics in quasi-one-dimensional lattices is studied by calculating the persistent current in small quantum rings and by exact simulations of the timeevolution of the many-particle state in two cases: Expansion of a localized cloud, and collisions in a Newtons cradle. We consider three different lattices which in the tight binding model exhibit flat bands. The physical realization is considered to be an optical lattice with bosonic or fermionic atoms. The atoms are assumed to interact with a repulsive short range interaction. The different statistics of bosons and fermions lead to different dynamics. Spinless fermions are easily trapped in the flat-band states due to the Pauli exclusion principle, which prevents them from interacting, while bosons are able to push each other out from the flat-band states.

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Section: Introductionmentioning

confidence: 99%

Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices

2013

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“…We shall discuss finally on the effect of the electron-electron interaction on the localization of many-electron wave-packets. AB cages in two-dimensional and quasione-dimensional bipartite lattices have been proven to be robust against a small but sizeable disorder and the presence of on-site potentials [29,30,31], but become rapidly unbound as soon as the electrons interact, owing to the generation of extended manyparticle states [30,32]. However, the close agreement between our numerical results and those derived from the one-dimensional TB model provides evidence that the localization phenomenon addressed here should persist in the presence of low or even moderate electron-electron interactions.…”

Section: Resultsmentioning

confidence: 99%

Magnetic modulation of the tunnelling between defect states in antidot superlattices

Movilla¹,

Planelles²

2012

J. Phys.: Condens. Matter

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Abstract. We show theoretically that the tunneling between properly designed defects in periodic antidot lattices can be strongly modulated by applied magnetic fields. Further, transport channels made up of linear arrangements of tunnel-coupled defects can accomodate Aharonov-Bohm cages, suggesting a magnetic control of the transport through the system. Evidence supporting an unusual robustness of the caging effect against electron-electron interactions is also provided.

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“…As a result, the conductivity vanishes, at least on the noninteracting level. This accords with the vanishing Chern number of strictly flat single particle bands where dε k /dk = 0 , throughout the Brillouin zone, as proven recently [7] for tight binding lattices.On-site Hubbard interaction seems to delocalize vicinally caged carriers, which was considered as indication for nonzero conductivity [8]. However, short range interactions cannot impair the huge flat band degeneracy at low fillings [9].…”

mentioning

confidence: 99%

“…On-site Hubbard interaction seems to delocalize vicinally caged carriers, which was considered as indication for nonzero conductivity [8]. However, short range interactions cannot impair the huge flat band degeneracy at low fillings [9].…”

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confidence: 99%

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Flat-band conductivity properties at long-range Coulomb interactions

Häusler

2015

Phys. Rev. B

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Dispersionless (flat) electronic bands are investigated regarding their conductance properties. Due to "caging" of carriers these bands are usually insulating at partial filling, at least on the non-interacting level. Considering the specific example of a T3-lattice we study long-range Coulomb interactions. A non-trivial dependence of the conductivity on flat band filling is obtained, exhibiting an infinite number of zeros. Near these zeros, the conductivity rises linearly with carrier density. At densities half way in between adjacent conductivity-zeros, strongly enhanced conductivity is predicted, accompanying a solid-solid phase transition.PACS numbers: 71.10. Fd,73.20.Qt,73.20.Jc,73.90.+f Recently, electronic flat bands in periodic lattices have received considerable attention [1], where single particle energies ε k of at least one tight binding band stay non-or weakly dispersing, throughout the Brillouin zone. One focus of interest in two spatial dimensions, similar to Landau levels, is the effect of interactions which in the absence of kinetic energy always has to be treated nonperturbatively. Fractional Chern insulator (FCI) phases have been identified [2,3], some of which exhibit Chern numbers larger than unity [4] and thereby generalize fractional quantum Hall states. Meanwhile, many lattices have been detected to host flat bands. Band flatness [5] arises due to localization by local quantum interferences, coined [6] as "caging" of carriers. As a result, the conductivity vanishes, at least on the noninteracting level. This accords with the vanishing Chern number of strictly flat single particle bands where dε k /dk = 0 , throughout the Brillouin zone, as proven recently [7] for tight binding lattices.On-site Hubbard interaction seems to delocalize vicinally caged carriers, which was considered as indication for nonzero conductivity [8]. However, short range interactions cannot impair the huge flat band degeneracy at low fillings [9]. Competing charge density wave phases have been studied [3]. Here, we investigate long range Coulomb interactions which at any filling will lift the flat band degeneracy. In quantum Hall systems, when kinetic energy is quenched, they cause Wigner crystallization at fillings ν < 1 /5 [10] (in graphene at ν < 0.28 [11]) while without magnetic field crystallization appears when the Coulomb energy E C exceeds the kinetic energy E K by a sufficiently big factor [12], E C /E K > 37 . The longitudinal conductivityof clean systems at zero temperature diverges [13] and is then due to sliding of the hexagonal crystal as a whole [14]. Its Drude weight D = e 2 n/m is determined by carrier density n and particle masses m, just as in the absence of interactions [15]; in this work we do not con- sider crystalline disorder. In flat bands, where no kinetic energy competes, we always expect a Wigner crystallized phase. Conductance properties, quantified again by the Drude weight D, cannot simply be proportional to m −1 since m is a priori meaningless to parameterize kinetic energy [5]. In ...

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Interaction Induced Delocalization for Two Particles in a Periodic Potential

Cited by 172 publications

References 12 publications

Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices

Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices

Magnetic modulation of the tunnelling between defect states in antidot superlattices

Flat-band conductivity properties at long-range Coulomb interactions

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