## The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

Pietro Silvi, Ferdinand Tschirsich, Matthias Gerster, Johannes Jünemann, Daniel Jaschke, Matteo Rizzi, Simone Montangero

SciPost Phys. Lect. Notes 8 (2019) · published 18 March 2019

- doi: 10.21468/SciPostPhysLectNotes.8
- Submissions/Reports

### 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-dimension 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.

### Cited by 8

### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1 }^{2 }Pietro Silvi, -
^{2 }Ferdinand Tschirsich, -
^{2 }Matthias Gerster, -
^{3 }Johannes Jünemann, -
^{2 }^{4 }Daniel Jaschke, -
^{3 }Matteo Rizzi, -
^{2 }^{5 }^{6 }Simone Montangero

^{1}Universität Innsbruck / University of Innsbruck [UBI]^{2}Universität Ulm / University of Ulm^{3}Johannes Gutenberg-Universität Mainz / Johannes Gutenberg University of Mainz^{4}Colorado School of Mines [CSM]^{5}Universität des Saarlandes / Saarland University^{6}Università degli Studi di Padova / University of Padua [UNIPD]

- Baden-Württemberg Stiftung
- Carl-Zeiss-Stiftung / Carl Zeiss Foundation
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- European Research Council [ERC]
- FP7 Information and Communication Technologies (FP7 ICT) (through Organization: European Commission [EC])
- H2020 Future and Emerging Technologies (FET) (through Organization: European Commission [EC])
- Studienstiftung des Deutschen Volkes (through Organization: Studienstiftung des deutschen Volkes / German National Academic Foundation)