Preformed pairs in flat Bloch bands

TL;DR

This paper demonstrates that in flat Bloch bands, only bound pairs of particles propagate, leading to a half-flux quantum periodicity in the ground state energy, indicating preformed pairs dominate transport even above superfluid transition temperatures.

Contribution

The study provides numerical and analytical evidence that in flat band lattice models, bound pairs of particles are the primary propagating entities, with a novel half-flux quantum periodicity in the energy spectrum.

Findings

Ground state energy exhibits half-flux quantum period, indicating pair propagation.

Analytical proof that the entire many-body spectrum shares this periodicity.

Existence of extensive conserved quantities related to localized quasiparticle states.

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. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum $\Phi_0/2 = hc/(2e)$ period, indicating that only bound pairs of particles with charge $2e$ are propagating, while single quasiparticles with charge $e$ remain localized. We show analytically in one dimension 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 we construct an extensive number of exact conserved quantities for the one dimensional lattice models. These conserved quantities are associated to the occupation of localized single quasiparticle states. Our results imply that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state.