Preliminary list of abstracts

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Approximation techniques for special eigenvalue problems
Keywords: Tensor decomposition schemes; Matrix Product States; Truncation
Wed, 16:10--16:35
  • Waldherr, Konrad (Institute of Computer Science, TU München, Germany)
  • Huckle, Thomas (Institute of Computer Science, TU München)
  • Schulte-Herbrüggen, Thomas (Institute of Chemistry, TU München)

The computation of the ground state (i.e. the eigenvector related to the smallest eigenvalue) is an important task when dealing with quantum systems. As the dimension of the underlying vector space grows exponentially in the number of physical sites, one has to consider appropriate subsets promising both convenient approximation properties and efficient computations.

For $1$D systems, Matrix Product States (MPS) are in use. Algorithms based on MPS only scale polynomially in the size of the physical system, but still guarantee to approximate ground states faithfully. As the set of Matrix product states is not closed under addition, we need techniques that allow us to project a sum of MPS back onto the MPS space, which turns out to be a highly nonlinear approximation problem.

We will use two methods of how to truncate a given large MPS representation to a smaller one. Furthermore, we will present applications of such compression techniques to numerical methods for solving the above eigenvalue problems.