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.

Dimension of tensor network varieties / Bernardi, A.; De Lazzari, C.; Gesmundo, F.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 2023, 25:10(2023), pp. 225005901-225005931. [10.1142/S0219199722500596]

Dimension of tensor network varieties

Bernardi, A.;De Lazzari, C.
;
2023-01-01

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.
2023
10
Bernardi, A.; De Lazzari, C.; Gesmundo, F.
Dimension of tensor network varieties / Bernardi, A.; De Lazzari, C.; Gesmundo, F.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 2023, 25:10(2023), pp. 225005901-225005931. [10.1142/S0219199722500596]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/372549
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