A variational approach to the three-body problem in the Hubbard model. Exact result

E. G. Goryachev, E. Yankovsky

M. Iskin

M. Heise, Rainer J. Jelitto

Sigrid M. Weber, H. Büttner

M. Iskin

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-$\ensuremath{\uparrow}$ fermions and a spin-$\ensuremath{\downarrow}$ fermion due to an on-site 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.

Jun-ichi Igarashi, Tatsuya Nagao

We propose an approximate version of the three-body scattering theory as an extension of local approximation. We solve the three-body problem by limiting the number of three-body states, instead of solving the Faddeev equation, in the calculation of the self-energy. Applying this simple extension to the antiferromagnetic state at half-filling in the two-dimensional Hubbard model, we demonstrate that it gives a reasonable spectral function for the single-particle Green's function in comparison with the results of the exact diagonalization for finite clusters and the quantum Monte Carlo method. We also show that it gives the ground state energy and the sublattice magnetization comparable to previous variational Monte Carlo results.