Particle Number Conservation and Block-Sparse Matrix Product States

Markus Bachmayr
Johannes Gutenberg-Universität Mainz

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. Finally, we discuss their application in low-rank eigensolvers using full residual information.
Joint work with Michael Götte and Max Pfeffer.

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