Strongly bound fermion pairs on a ring: a composite-boson approach

TL;DR

This paper investigates the validity of the coboson formalism for describing bound fermion pairs on a ring, revealing its limitations in one-dimensional systems and proposing ways to improve the treatment of composite bosons.

Contribution

It analyzes the conditions under which the coboson ansatz fails in 1D systems and demonstrates how to recover the correct ground state, enhancing the formalism's applicability.

Findings

The coboson ansatz can fail in 1D systems expected to be valid.

The formalism can be corrected to recover the true ground state.

Highlights limitations and strengths of coboson theory.

Abstract

Particles made of two fermions can in many cases be treated as elementary bosons, but the conditions for this treatment to be valid are nontrivial. The so-called "coboson formalism" is a powerful tool to tackle compositeness effects relevant for instance for exciton physics and ultracold atomic dimers. A key element of this theory is an ansatz for the ground state of N pairs, built from the single-pair ground state combined with the exclusion principle. We show that this ansatz can fail in one-dimensional systems which fulfill the conditions expected to make the ansatz valid. Nevertheless, we also explain how coboson theory can recover the correct ground state. Thus, our work highlights limitations and strengths of the formalism and leads to a better treatment of composite bosons.