Comparing few-body interactions in the Bose-Hubbard model using bipartite entanglement

This study investigates the Bose-Hubbard Model in one dimension and compares the effects of three different forms of interactions: two-body, three-body interactions, and a peculiar form of non-local four-body interactions between bosons. These three interactions are the lattice versions of all topologically relevant or marginal interactions possible in one dimension and, in the continuum, have been shown to influence effective particle statistics and support anyonic solutions. Through exact diagonalization, we explore how each of these affects the energy, degeneracy, and entanglement properties of the system. By employing the one-body reduced density matrix and calculating bipartite entanglement on a lattice, we compare the differential impacts on the quantum correlations between distinct subsystems.