Effective theory for strongly attractive one-dimensional fermions

TL;DR

This paper develops an effective theory for strongly attractive one-dimensional fermions, simplifying the complex many-body problem into a weakly interacting model using Bethe ansatz solutions, enabling easier analysis of such systems.

Contribution

It introduces a novel effective theory that maps strongly interacting fermions and dimers onto a weakly interacting model, facilitating perturbative approaches.

Findings

Analytical solutions for few-body scattering via Bethe ansatz.

Effective interactions can be mapped onto a weakly interacting problem.

Simplifies the study of many-fermion systems under confinement.

Abstract

We study a one-dimensional system of two-component fermions in the limit of strong attractive particle-particle interactions. First, we analyze scattering in the corresponding few-body problem, which is analytically solvable via Bethe ansatz. This allows us to engineer effective interactions between the system's effective degrees of freedom: fermions and bosonic dimers (tightly bound pairs of fermions). We argue that, although these interactions are strong, the resulting effective problem can be mapped onto a weakly interacting one, paving the way for the use of perturbation theory. This finding simplifies studies of many-fermion systems under confinement that are beyond reach of state-of-the-art numerical methods. We illustrate this statement by considering an impurity atom in a Fermi gas.