Effective theory for strongly attractive one-dimensional fermions
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.
Cite
@article{arxiv.2412.05915,
title = {Effective theory for strongly attractive one-dimensional fermions},
author = {Timothy G. Backert and Fabian Brauneis and Matija Čufar and Joachim Brand and Hans-Werner Hammer and Artem G. Volosniev},
journal= {arXiv preprint arXiv:2412.05915},
year = {2025}
}
Comments
Version accepted for publication in Physical Review Letters