Abstract for the talk on 21.06.2018 (15:15 h)


André Uschmajew (MPI MIS, Leipzig)
Low-rank approximability of nearest neighbor interaction systems

Low-rank tensor techniques are an important tool for the numerical treatment of equations with a high-dimensional state space. Nearest neighbor interaction systems like the Ising model or some Chemical Master equations are examples for this, and the low-rank tensor train format has shown to be efficient for their computation in some cases. A challenging task, however, is to provide theoretical justification for this, that is, to show that the exact solutions (which are not computable due to high dimensionality) are indeed well approximable by low-rank tensors. For ground states of 1D quantum spin systems such arguments have been found in the theoretical physics community, but they apply more generally. The idea is to study the rank-increasing properties of polynomials of the nearest neighbor Hamiltonian, based on partial commutativity of the local operators. In this talk, we will explain this idea and present numerical examples.



23.06.2018, 02:30