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arXiv · 2101.03148

Dimension of Tensor Network varieties

Alessandra Bernardi·Claudia De Lazzari·Fulvio Gesmundo
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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.

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Alessandra Bernardi, Claudia De Lazzari, Fulvio Gesmundo. 2021-01-08. Dimension of Tensor Network varieties. https://doi.org/10.1142/s0219199722500596

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