Méthodes de calcul avec réseaux de tenseurs en physique (Basic tensor network computations in physics)
arXiv:1911.11566 · doi:10.1139/cjp-2019-0611
Abstract
Cet article se veut un survol des réseaux de tenseurs et s'adresse aux débutants en la matière. Nous y mettons l'accent sur les outils nécessaires à l'implémentation concrète d'algorithmes. Quatre opérations de base (remodelage, permutation d'indices, contraction et décomposition) qui sont couramment utilisées dans les algorithmes de réseaux de tenseurs y sont décrites. Y seront aussi couverts la notation diagrammatique, les états en produit de matrices (MPS), les opérateurs en produit de matrices (MPO), état projeté de paires intriquées (PEPS), l'approche par renormalisation d'enchevêtrement multi-échelle (MERA), la décimation par bloc d'évolution temporelle (TEBD) et le groupe de renormalisation de tenseurs (TRG). This article is intended as an overview of tensor networks for beginners looking to perform computations. We focus on the tools necessary for the concrete implementation of algorithms. Four basic operations (reshaping, permutation, contraction, and decomposition) that are commonly used in tensor network algorithms are covered. The article also briefly reviews diagrammatic notation, matrix product states (MPS), matrix product operators (MPO), projected entangled pair states (PEPS), multi-scale entanglement renormalization ansatz (MERA), time evolution block decimation (TEBD), and tensor renormalization group (TRG).
arXiv commentFrançais (1-19) English (20-36) 36 pages total, 36 figures total
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