Correlated metallic two-particle bound states in Wannier-Stark flatbands

Abstract

Tight-binding single-particle models on simple Bravais lattices in space dimension d 2, when exposed to commensurate DC fields, result in the complete absence of transport due to the formation of Wannier-Stark flatbands [Phys. Rev. Res. 3, 013174 (2021)]. The single-particle states localize in a factorial manner, i.e., faster than exponential. Here, we introduce interaction among two such particles that partially lifts the localization and results in metallic two-particle bound states that propagate in the directions perpendicular to the DC field. We demonstrate this effect using a square lattice with Hubbard interaction. We apply perturbation theory in the regime of interaction strength (U) << hopping strength (h) << field strength (F), and obtain estimates for the group velocity of the bound states in the direction perpendicular to the field. The two-particle group velocity scales as U(h/F)v. We calculate the dependence of the exponent von the DC field direction and on the dominant two-particle configurations related to the choices of unperturbed flatbands. Numerical simulations confirm our predictions from the perturbative analysis.