Constraining the particle number (or other quantum numbers) in matrix product states leads to a block-sparsity pattern in tensor components. This is exploited in many tensor network codes, in particular in DMRG algorithms. In this talk, we look at such block-sparsity properties from a more general point of view, with potential applications in other contexts. We then consider the interaction of the block structure with matrix product operator representations of Hamiltonians in quantum chemistry. We obtain explicit representations of such Hamiltonians operating directly on the block structures, with improved rank bounds under sparsity assumptions on the Hamiltonian coefficients, and a matrix-free implementation operating directly on block structures. In addition, we discuss the joint parameterization of several eigenspaces in this format, its use in eigenvalue solvers, and further applications.
Joint work with Michael Götte and Max Pfeffer.
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