Assembly of 2N entangled fermions into multipartite composite bosons

An even number of fermions can behave in a bosonic way. The simplest scenario involves two fermions which can form a single boson, but four fermions can either behave as two bipartite bosons or further assemble into a single four-partite bosonic molecule. In general, for 2N fermions there are many possible arrangements into composite bosons. What determines which fermionic arrangement is realized in a given situation, and is it truly bosonic? This paper aims to answer the above question. We propose an entanglement-based method to assess bosonic quality of fermionic arrangements and apply it to study how the ground state of the extended one-dimensional Hubbard model changes as the strength of interparticle interactions increases.