Preformed pairs in flat Bloch bands

Murad Tovmasyan, Sebastiano Peotta, Long Liang, Päivi Törmä, Sebastian D. Huber

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Abstract

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.
Original languageEnglish
Article number134513
Pages (from-to)1-22
JournalPhysical Review B
Volume98
Issue number13
DOIs
Publication statusPublished - 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Condensed Matter - Strongly Correlated Electrons
  • Condensed Matter - Quantum Gases
  • Condensed Matter - Superconductivity

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