Affiliation:
1. University of Innsbruck
2. University of Ulm
3. Johannes Gutenberg University of Mainz
4. Colorado School of Mines
5. Saarland University
6. University of Padua
Abstract
We present a compendium of numerical simulation techniques, based on
tensor network methods, aiming to address problems of many-body quantum
mechanics on a classical computer. The core setting of this anthology
are lattice problems in low spatial dimension at finite size, a physical
scenario where tensor network methods, both Density Matrix
Renormalization Group and beyond, have long proven to be winning
strategies. Here we explore in detail the numerical frameworks and
methods employed to deal with low-dimensional physical setups, from a
computational physics perspective. We focus on symmetries and
closed-system simulations in arbitrary boundary conditions, while
discussing the numerical data structures and linear algebra manipulation
routines involved, which form the core libraries of any tensor network
code. At a higher level, we put the spotlight on loop-free network
geometries, discussing their advantages, and presenting in detail
algorithms to simulate low-energy equilibrium states. Accompanied by
discussions of data structures, numerical techniques and performance,
this anthology serves as a programmer’s companion, as well as a
self-contained introduction and review of the basic and selected
advanced concepts in tensor networks, including examples of their
applications.
Funder
Baden-Württemberg Stiftung
Carl-Zeiss-Stiftung
Deutsche Forschungsgemeinschaft
European Research Council
FP7 Information and Communication Technologies
H2020 Future and Emerging Technologies
Studienstiftung des Deutschen Volkes
Cited by
66 articles.
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