Dresden 2017 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 5: Correlated Electrons: (General) Theory 1
TT 5.7: Vortrag
Montag, 20. März 2017, 11:15–11:30, HSZ 304
Generic Construction of Efficient Matrix Product Operators — •Claudius Hubig1, Ian McCulloch2, and Ulrich Schollwöck1 — 1Department of Physics and Arnold Sommerfeld Center for Theoretical Physics,Ludwig-Maximilians-Universität München, Germany — 2Centre for Engineered Quantum Systems, School of Physical Sciences, The University of Queensland, Brisbane, Australia
Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We give an introduction to arithmetic with general MPOs and compression of general MPOs. We show that it is possible to generate optimal representations of a wide class of Hamiltonians using a very generic construction method, including powers of short-range one-dimensional Hamiltonians, Hamiltonians for two-dimensional systems and as a proof of principle, the long-range four-body Hamiltonian from quantum chemistry. The construction method consists of the definition of single-site operators, implementation of generic MPO arithmetic for addition and multiplication and the use of three compression methods (Rescaled SVD, Deparallelisation and Delinearisation) to achieve the most efficient MPO representation.