IWR Colloquium Summer Semester 2025 Multilayer Multiconfiguration Time-Dependent Hartree Theory

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory is a powerful and versatile method for simulating quantum dynamics in high-dimensional systems. This numerical approach is based on the time-dependent variational principle and employs a flexible, hierarchical representation of the wavefunction. Specifically, the wavefunction is recursively expanded in a tree-like structure with dynamically optimized layers, enabling an efficient description of complex many-body quantum correlations. Mathematically, this representation corresponds to the hierarchical Tucker tensor decomposition, though in practice, the latter often employs a balanced binary tree structure. A special case involving a skewed tree is known in the mathematics literature as the tensor train format, and in physics as the matrix product state (MPS) representation. In this talk, I will present an overview of the ML-MCTDH theory, discuss its computational performance, and illustrate its application to model reactions that exhibit significant many-body quantum effects.