  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. The question is: what determines
which fermionic arrangement is going to be realized in a given situation and
can such arrangement be considered truly bosonic? This work aims to find the
answer to 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
intra-particle interactions increases.
