A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom

A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom

We present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already versed with their theoretical foundations. These skills include...

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Bibliographic Details
Published in:Frontiers in applied mathematics and statistics Vol. 8
Main Author: Evenbly, Glen
Format: Journal Article
Language:English
Published: Frontiers Media S.A 01-06-2022
Subjects:
DMRG
MPS
quantum many body theory
tensor contraction
tensor network algorithm
Online Access:Get full text
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Summary:We present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already versed with their theoretical foundations. These skills include an introduction to the contraction of tensor networks, to optimal tensor decompositions, and to the manipulation of gauge degrees of freedom in tensor networks. The topics presented are of key importance to many common tensor network algorithms such as DMRG, TEBD, TRG, PEPS, and MERA.
ISSN:2297-4687
2297-4687
DOI:10.3389/fams.2022.806549