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Graph Equitable Partitioning in Quantum Many-Body Physics

David Feder, University of Calgary

(Session 7c : Friday from 4:00 - 4:30)

Abstract. The Hamiltonian for bosonic and fermionic particles hopping on lattices can be interpreted as the adjacency matrix of an undirected, weighted graph, usually with self-loops. The properties of these quantum many-body systems can therefore be analyzed in terms of graph theory. For example, the simple graph for non-interacting distinguishable particles is the Cartesian product of each particle's adjacency matrix; if these particles become indistinguishable, the graph 'collapses' via a graph equitable partition. Under various circumstances, equitable partitioning can allow for a more efficient determination of the eigenstates (and therefore the properties) of physically interesting quantum many-body systems. I will focus in particular on the ground states of the Bose and Fermi Hubbard models.