Regensburg 2016 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 61: Correlated Electrons: (General) Theory 1

TT 61.13: Vortrag

Donnerstag, 10. März 2016, 12:45–13:00, H18

DMRG Application in Binary Tree Tensor Networks with Non-Abelian Symmetries — •Claudius Hubig and Ulrich Schollwöck — Department für Physik, LMU München, Germany

The density matrix renormalisation group (DMRG) algorithm and the underlying matrix product state (MPS) state representation have become the workhorse of numerical solid state physics in one dimension. Generalisations to two and more dimensions have been realised as general tensor networks. Of these, binary tree tensor networks preserve most of the favourable properties of MPS while already allowing for a strikingly different entanglement structure. This is in particular relevant in the context of dynamical mean-field theory, where DMRG-based solvers have been employed recently, but were hindered by the one-dimensional structure of MPS.

This contribution discusses the implementation and performance behaviour of DMRG and related methods for binary tree tensor networks which identically conserve both abelian and non-abelian symmetries, such as U(1)_Charge and SU(2)_Spin. Numerical exploitation of these symmetries directly leads to large speed-ups and further simplifies parallelisation over many cores.