Stars & Bars: A Compact Representation for Bosonic Occupation States

An efficient representation of occupation states of particles on lattices is a critical tool for the exact diagonalization of bosonic Hamiltonians. The memory demands of the traditional method of representing such systems, as arrays of integers, increases rapidly as system size grows, limiting current studies to approximately 16 particles at unit filling. Representing basis vectors using the stars and bars method of combinatorics 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