Bound states of a system of two fermions on a one-dimensional lattice

P. E. Kornilovitch

Saidakhmat Norzhigitovich Lakaev, Sh. I. Khamidov, Собир Сахибжанович Улашов

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.

J. I. Abdullaev, Berdiyor Mamirov

In this paper, the Hamiltonian of the system of two fermions on the three-dimensional lattice 3 is considered. Under some conditions to the potential, it is proven that H (k) has four invariant subspaces: in one of them H ( k ) coincides with H 0 ( k ) and the restrictions of H ( k ) to the rests three subspaces are unitarily equivalent to each other. Moreover, for the eigenvalues and eigenfunctions of these restricted operators explicit expressions are found.

Taku Matsui

Yuchi He, Binbin Tian, David Pekker +1 more

We study the formation of bound states in a one-dimensional, single-component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of three-fermion bound states (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a two-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the two-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.

K. Kilimann, D. Kremp, G. Röpke