Three-body problem in a multiband Hubbard model

TL;DR

This paper investigates the three-body problem in a multiband lattice, deriving exact solutions and revealing stable trimer states with flat dispersion in flat bands, contrasting with single-band models.

Contribution

It introduces a variational approach to solve the three-body problem in multiband lattices and demonstrates the existence of stable trimers with unique dispersion properties.

Findings

Stable trimers exist in two-band models, unlike single-band chains.

Trimers in flat bands exhibit nearly-flat dispersion.

Theoretical framework reduces to an eigenvalue problem.

Abstract

We consider the three-body problem in a generic multiband lattice, and analyze the dispersion of the trimer states that are made of two spin-$\uparrow$ fermions and a spin-$\downarrow$ fermion due to an onsite attraction in between. Based on a variational approach, we first obtain the exact solution in the form of a set of coupled integral equations, and then reduce it to an eigenvalue problem. As an illustration we apply our theory to the sawtooth lattice, and numerically show that energetically-stable trimers are allowed in a two-band setting, which is in sharp contrast with the single-band linear-chain model. In particular we also reveal that the trimers have a nearly-flat dispersion when formed in a flat band, which is unlike the highly-dispersive spectrum of its dimers.