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An even number of fermions can behave in a bosonic way. The simplest scenarioinvolves two fermions which can form a single boson. But four fermions caneither behave as two bipartite bosons or further assemble into a singlefour-partite bosonic molecule. In general, for 2N fermions there are manypossible arrangements into composite bosons. The question is: what determineswhich fermionic arrangement is going to be realized in a given situation andcan such arrangement be considered truly bosonic? This work aims to find theanswer to the above question. We propose an entanglement-based method to assessbosonic quality of fermionic arrangements and apply it to study how the groundstate of the extended one-dimensional Hubbard model changes as the strength ofintra-particle interactions increases.

Assembly of 2N entangled fermions into multipartite composite bosons