IGPM (RWTH Aachen)
Wednesday, June 3rd, 2026 at 3:30 CET (Paris time).
Block-Sparse Matrix Product States and Eigenvalue Solvers
Based on joint works with Michael Götte, Sebastian Krämer and Max Pfeffer.
Constraining the particle number (or other quantum numbers) in matrix product states leads to a block-sparsity pattern in tensor components that is exploited in many tensor network codes. In this talk, we look at such block-sparsity properties from the perspective of numerical analysis, considering in particular 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. We then turn to low-rank preconditioned eigensolvers with convergence guarantees and quasi-optimal rank bounds in the context of such block-sparse representations.