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arXiv · 2201.13139

Three-body problem in a multiband Hubbard model

M. Iskin
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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.

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M. Iskin. 2022-01-31. Three-body problem in a multiband Hubbard model. https://doi.org/10.1103/physreva.105.063310

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