Preformed pairs in flat Bloch bands

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.

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

“…We also expect similar phenomena in other flat-band models, such as the saw-tooth, diamond and Lieb lattice models, which are to be realized in experiments [70][71][72][73][74], and also some studies in the Creutz ladder in the clean limit [75,76] pointed out the presence of conserved quantities. Such conjecture may support our results.…”

Pairing and superconductivity in the flat band: Creutz lattice

“…Note. Upon completion of this manuscript, a preprint appeared which tackled a similar problem [45], also finding formation of pair superfluidity away from half-filling. In addition to obtaining similar results, here we also quantitatively connect the results in the strongly interacting regime to a repulsive hardcore boson model which is superfluid for any finite interactions.…”

Pairing and non-Fermi liquid behavior in partially flat-band systems: Beyond nesting physics

“…While there is a long history for the study of flat-band systems as initiated by interests in ferromagnetism [1][2][3][4][5] , there is a recent surge of interests in flat-band superconductivity, where possibilities are explored for unconventional superconductivity favored by the flat-band structure [6][7][8][9] . As for attractive electron-electron interactions, Törmä's group has shown that a flat band can indeed favor superconductivity when the band is topological, with the superfluid weight lower-bounded by the topological number [10][11][12][13][14] . For repulsive interactions, on the other hand, a key question is how the presence of flat bands affects electron correlation processes.…”