Time integration of tree tensor networks
Vortrag von Prof. Dr. Christian Lubich
Datum: 20.05.26 Zeit: 16.30 - 18.00 Raum: ETH HG G 19.2
| The talk first presents some numerical experiments with time-dependent tree tensor network algorithms for the approximation of quantum spin system dynamics. It continues with the basics in the design of time integration methods that are robust to the typical 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 for parallelism. This discussion of basic concepts forms the main part of the talk and will be done for the smallest possible type of tensor network differential equations, namely low-rank matrix differential equations, which are of interest in their own right. Once this nontrivial technically simplest case is understood, there is a systematic path to the extension of the integrators and their favourable properties to general tree tensor networks. This talk is based on joint work with many colleagues and former and present students, among which I wish to single out Othmar Koch for the first mathematical work on dynamical low-rank approximation (DLRA) in 2007, Ivan Oseledets for jointly discovering the first robust DLRA integrator in 2014 (the projector-splitting integrator), Gianluca Ceruti and Jonas Kusch for jointly developing the Basis Update & Galerkin (BUG) integrators since 2022, and Hanna Walach, Gianluca Ceruti, Dominik Sulz and Charlotte Verhoeven for the recent systematic extension from low-rank matrices to general tree tensor networks both in theory and in increasingly efficient implementations. |