Dimension of Tensor Network varieties
arXiv:2101.03148 · doi:10.1142/S0219199722500596
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.
arXiv comment27 pages, 3 figures. Final version, to appear in Communications in Contemporary Mathematics
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