Mathematical and Numerical Aspects of Quantum Dynamics

Evolution of quantum many-body systems using tensor network states

Thomas Barthel

Duke University

Tensor network states are a numerical approach for the simulation of strongly correlated quantum many-body systems. As the computation costs are intimately related to entanglement properties of these systems, I will discuss how entanglement entropies scale in time-evolved states. For quasi-1d systems, matrix product state techniques allow us to study dynamics in closed systems, open quantum systems, and systems at finite temperatures. Especially with respect to the investigation of response functions, corresponding, for example, to experimental X-ray and neutron scattering spectra, I will describe recently developed tricks to tackle the entanglement growth barrier and reach long times.