# Preformed pairs in flat Bloch bands

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**Preformed pairs in flat Bloch bands.** / Tovmasyan, Murad; Peotta, Sebastiano; Liang, Long; Törmä, Päivi; Huber, Sebastian D.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Physical Review B*, vol. 98, no. 13, 134513, pp. 1-22. https://doi.org/10.1103/PhysRevB.98.134513

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*Physical Review B*,

*98*(13), 1-22. [134513]. https://doi.org/10.1103/PhysRevB.98.134513

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TY - JOUR

T1 - Preformed pairs in flat Bloch bands

AU - Tovmasyan, Murad

AU - Peotta, Sebastiano

AU - Liang, Long

AU - Törmä, Päivi

AU - Huber, Sebastian D.

N1 - | openaire: EC/H2020/702281/EU//FLATOPS

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Condensed Matter - Strongly Correlated Electrons

KW - Condensed Matter - Quantum Gases

KW - Condensed Matter - Superconductivity

UR - https://arxiv.org/abs/1805.04529

U2 - 10.1103/PhysRevB.98.134513

DO - 10.1103/PhysRevB.98.134513

M3 - Article

VL - 98

SP - 1

EP - 22

JO - Physical Review B (Condensed Matter and Materials Physics)

JF - Physical Review B (Condensed Matter and Materials Physics)

SN - 2469-9950

IS - 13

M1 - 134513

ER -

ID: 21096544