Stars & Bars: A Compact Representation for Bosonic Occupation States

An efficient representation of bosonic occupation states is a critical tool for the exact diagonalization of bosonic Hamiltonians. The memory demands of the traditional method of representing such systems, as lexicographically ordered arrays of integers, increases rapidly as system size grows, limiting current studies to approximately 16 particles at unit filling. Representing basis vectors using the combinatoric stars and bars method allows each basis state to be stored as a single 64 bit integer. This optimally compact representation will enable the analysis of new properties of larger bosonic Hamiltonians, including accessible entanglement, which may be useful in evaluating many-body phases as potential candidate quantum resource states.