Abstract
We associate a bosonic network to each complete bipartite graph. A Hamiltonian is defined with hopping terms on the edges of the graph, and a global interaction term depending on the vertex sets. For a generic graph this Hamiltonian is superintegrable, and we derive a Bethe Ansatz solution for the energy and eigenstates. These results provide the means to investigate the quantum dynamics and allow for the computation of occupancy probabilities in certain regimes. We use these results to gain an understanding of entanglement evolution in the network.
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