Speaker: Dominik Sulz University of Tübingen (host: Legeza Örs)
Title: Many-body Quantum Dynamics using Tree Tensor Networks
Date: Tuesday, 26 May 2024, 13:00
Place: KFKI Campus, Bldg. 1, 2nd floor, Conference Room
Abstract:
In many applications, it is of interest to numerically solve high-order tensor differential equations, e.g. the many-body Schrödinger equation in quantum physics or discretized high-dimensional time-dependent partial differential equations. Tree tensor networks (TTNs) turned out to be a promising ansatz to overcome the so-called "curse of dimensionality'' as they are an efficient hierarchical data sparse format to approximate tensors. Based on the dynamical low-rank approximation, several novel time integration methods for TTNs have been proposed in the last few years. In a recursion from the leaves up to the root, all nodes are updated by only solving small matrix-/tensor differential equations. The proposed methods are robust even in the presence of small singular values. Further properties like rank-adaptivity, norm and energy preservation and error behaviour are mathematically are discussed.
The talk intends to give an overview of the latest results for dynamical low-rank approximations. Further, the different time integration methods and their applicability to many-body quantum systems are discussed. Numerical experiments validate the theoretical results and show several applications from quantum physics.
