Abstract
We consider a system of three particles consisting of two identical fermions and one other particle on a one-dimensional lattice. The fermions interact via a nearest-neighbor potential of strength \(\mu_1\in\mathbb{R}\) , while the interaction between a fermion and one other particle is via an on-site potential with strength \({\mu_2\in\mathbb{R}}\) . We establish existence of bound states of the associated three-body lattice Schrödinger operator for all values of the total quasimomentum \(K\in\mathbb{T}^1\) . Furthermore, we show that both the bound state \(f_{\mu_1\mu_2}(K;\,{\cdot}\,{,}\,{\cdot}\,)\) and its corresponding eigenvalue \(E_{\mu_1\mu_2}(K)\) depend holomorphically on the quasimomentum.
