Pietro Silvi, Ferdinand Tschirsich, Matthias Gerster, Johannes Jünemann, Daniel Jaschke, Matteo Rizzi, Simone Montangero
SciPost Phys. Lect. Notes 8 (2019) ·
published 18 March 2019

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We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of manybody 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 lowdimension physical setups, from a computational physics perspective. We focus on symmetries and closedsystem 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 loopfree network geometries, discussing their advantages, and presenting in detail algorithms to simulate lowenergy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a selfcontained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.
Mr Tschirsich: "We thank the referee for her/h..."
in Report on Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Tensor Networks