Hannover 2016 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 18: Quantum Information: Concepts and Methods III
Q 18.2: Vortrag
Dienstag, 1. März 2016, 11:15–11:30, e214
Tree Tensor Network algorithms: Simulating quantum many-body models on lattices in one and two dimensions — •Matthias Gerster1, Matteo Rizzi2, Pietro Silvi1, Rosario Fazio3, and Simone Montangero1 — 1Institute for Complex Quantum Systems, Ulm University, D-89069 Ulm, Germany — 2Johannes Gutenberg-Universität Mainz, Institut für Physik, D-55099 Mainz, Germany — 3NEST, Scuola Normale Superiore & Istituto Nanoscienze CNR, I-56126 Pisa, Italy
We present a tree tensor network algorithm suitable for numerically determining and characterizing ground states of quantum lattice models in one and two spatial dimensions. Our tensor network method has several attractive features, the most prominent one being the treatment of open and periodic boundary conditions on equal footage. Moreover, the loopless network geometry guarantees the existence of a stable and efficient energy minimization algorithm, and a moderate scaling of the computational cost with the refinement parameter (bond dimension). We also comment on strategies for implementing symmetries in the state architecture, allowing to reduce the computational demands and enabling precise targeting of conserved quantities. We demonstrate the usefulness of our technique by some benchmark results for paradigmatic lattice models like an Ising chain.