Dimension of Tensor Network varieties
Quantum Physics
2022-09-27 v2 Algebraic Geometry
Abstract
The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper bound is given in cases relevant for applications such as varieties of matrix product states and projected entangled pairs states. We provide a range (the "supercritical range") of the parameters where the upper bound is sharp.
Keywords
Cite
@article{arxiv.2101.03148,
title = {Dimension of Tensor Network varieties},
author = {Alessandra Bernardi and Claudia De Lazzari and Fulvio Gesmundo},
journal= {arXiv preprint arXiv:2101.03148},
year = {2022}
}
Comments
27 pages, 3 figures. Final version, to appear in Communications in Contemporary Mathematics