Effective Theory for Strongly Attractive One-Dimensional Fermions

Abstract

I discuss how to effectively describe a one-dimensional system of two-component fermions in the regime of strong attractive particle-particle interactions. First, we examine scattering in the corresponding few-body problem, which can be solved analytically using the Bethe ansatz. This approach enables us to engineer effective interactions between the system’s relevant degrees of freedom: fermions and bosonic dimers (tightly bound pairs of fermions). We argue that, despite the strength of these interactions, the resulting effective problem can be mapped onto a weakly interacting one, thereby facilitating the use of techniques such as perturbation theory. This insight simplifies the study of many-fermion systems under confinement, which are otherwise beyond the reach of state-of-the-art numerical methods.

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