Time integration of tree tensor networks

by Prof. Christian Lubich (University of Tuebingen)

Thursday 8 Jun 2023, 15:00 → 16:00 Europe/Rome

Rectorate/Building-Auditorium (GSSI)

Abstract

First I report on recent numerical experiments with time-dependent tree tensor network algorithms for the approximation of quantum spin systems. I will then describe the basics in the design of time integration methods that are robust to the usual presence of small singular values, that have good structure-preserving properties (norm, energy conservation or dissipation), and that allow for rank (= bond dimension) adaptivity and also have some parallelism. This discussion of basic concepts will be done for the smallest possible type of tensor network differential equations, namely low-rank matrix differential equations. Once this simplest case is understood, there is a systematic path to the extension of the integrators and their favourable properties to general tree tensor networks.