A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom
Glen Evenbly
Abstract
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.
Topics & Concepts
Tensor (intrinsic definition)Tensor decompositionKey (lock)Tensor contractionDegrees of freedom (physics and chemistry)Cartesian tensorComputer scienceTensor fieldAlgebra over a fieldMathematicsTensor densityExact solutions in general relativityPhysicsPure mathematicsMathematical analysisQuantum mechanicsComputer securityQuantum many-body systemsTensor decomposition and applicationsModel Reduction and Neural Networks